المؤلفون: Carrero-Vera, Karla, Cruz-Suárez, Hugo, Montes-de-Oca, Raúl

مصطلحات موضوعية: keyword:Markov decision process, keyword:total reward, keyword:fuzzy reward, keyword:trapezoidal fuzzy number, keyword:optimal stopping problem, keyword:gambling model, msc:90C40, msc:93C40

وصف الملف: application/pdf

Relation: mr:MR4467492; zbl:Zbl 07584152; reference:[1] Abbasbandy, S., Hajjari, T.: A new approach for ranking of trapezoidal fuzzy numbers.Comput. Math. Appl. 57 (2009), 413-419. MR 2488614; reference:[2] Ban, A. I.: Triangular and parametric approximations of fuzzy numbers inadvertences and corrections.Fuzzy Sets and Systems 160 (2009), 3048-3058. MR 2567092; reference:[3] Bartle, R. G.: The Elements of Integration.Wiley, New York 1995. MR 0200398; reference:[4] Bellman, R. E., Zadeh, L. A.: Decision-making in a fuzzy enviroment.Management Sci. 17 (1970), 141-164. MR 0301613; reference:[5] Cavazos-Cadena, R., Montes-de-Oca, R.: Existence of optimal stationary policies in finite dynamic programs with nonnegative rewards.Probab. Engrg. Inform. Sci. 15 (2001), 557-564. MR 1852975; reference:[6] Chen, S. H.: Operations of fuzzy numbers with step form membership function using function principle.Information Sci. 108 (1998), 149-155. Zbl 0922.04007, MR 1632503; reference:[7] Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets: Theory and Applications.World Scientific, Singapore 1994. MR 1337027; reference:[8] Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Control.Springer Science and Business Media, New York 2013. MR 3010569; reference:[9] Efendi, R., Arbaiy, N., Deris, M. M.: A new procedure in stock market forecasting based on fuzzy random auto-regression time series model.Information Sci. 441 (2018), 113-132. MR 3771167; reference:[10] Fakoor, M., Kosari, A., Jafarzadeh, M.: Humanoid robot path planning with fuzzy Markov decision processes.J. Appl. Res. Tech. 14 (2016), 300-310.; reference:[11] Furukawa, N.: Parametric orders on fuzzy numbers and their roles in fuzzy optimization problems.Optimization 40 (1997), 171-192. MR 1620380; reference:[12] Kurano, M., Yasuda, M., Nakagami, J., Yoshida, Y.: Markov decision processes with fuzzy rewards.In: Proc. Int. Conf. on Nonlinear Analysis, Hirosaki 2002, pp. 221-232. MR 1986973; reference:[13] López-Díaz, M., Ralescu, D. A.: Tools for fuzzy random variables: embeddings and measurabilities.Comput. Statist. Data Anal. 51 (2006), 109-114. MR 2297590; reference:[14] Pedrycz, W.: Why triangular membership functions?.Fuzzy Sets and Systems 64 (1994), 21-30. MR 1281283; reference:[15] Puri, M. L., Ralescu, D. A.: Fuzzy random variable.J. Math. Anal. Appl. 114 (1986), 402-422. MR 0833596; reference:[16] Puterman, M. L.: Markov Decision Processes: Discrete Stochastic Dynamic. First edition.Wiley-Interscience, California 2005. MR 1270015; reference:[17] Rezvani, S., Molani, M.: Representation of trapezoidal fuzzy numbers with shape function.Ann. Fuzzy Math. Inform. 8 (2014), 89-112. MR 3214770; reference:[18] Ross, S.: Dynamic programming and gambling models.Adv. Appl. Probab. 6 (1974), 593-606. MR 0347381; reference:[19] Ross, S.: Introduction to Stochastic Dynamic Programming.Academic Press, New York 1983. MR 0749232; reference:[20] Semmouri, A., Jourhmane, M., Belhallaj, Z.: Discounted Markov decision processes with fuzzy costs.Ann. Oper. Res. 295 (2020), 769-786. MR 4181708; reference:[21] Syropoulos, A., Grammenos, T.: A Modern Introduction to Fuzzy Mathematics.Wiley, New Jersey 2020.; reference:[22] Zadeh, L.: Fuzzy sets.Inform. Control 8 (1965), 338-353. Zbl 0942.00007, MR 0219427; reference:[23] Zeng, W., Li, H.: Weighted triangular approximation of fuzzy numbers.Int. J. Approx. Reason. 46 (2007), 137-150. MR 2362230

الاتاحة: http://hdl.handle.net/10338.dmlcz/150463

المؤلفون: Zhang, Yong-Chao

مصطلحات موضوعية: keyword:entry decision time, keyword:exit decision time, keyword:implementation delay, keyword:optimal stopping problem, keyword:viscosity solution, msc:60G40, msc:91B06, msc:91G80

وصف الملف: application/pdf

Relation: mr:MR3842960; zbl:Zbl 06945739; reference:[1] Applebaum, D.: Lévy Processes and Stochastic Calculus.Cambridge Studies in Advanced Mathematics 116, Cambridge University Press, Cambridge (2009). Zbl 1200.60001, MR 2512800, 10.1017/CBO9780511809781; reference:[2] Bar-Ilan, A., Strange, W. C.: Investment lags.Amer. Econ. Rev. 86 (1996), 610-622.; reference:[3] Boyarchenko, S., Levendorskiĭ, S.: Irreversible Decisions Under Uncertainty. Optimal Stopping Made Easy.Studies in Economic Theory 27, Springer, Berlin (2007). Zbl 1131.91001, MR 2370439, 10.1007/978-3-540-73746-9; reference:[4] Costeniuc, M., Schnetzer, M., Taschini, L.: Entry and exit decision problem with implementation delay.J. Appl. Probab. 45 (2008), 1039-1059. Zbl 1167.60008, MR 2484160, 10.1239/jap/1231340232; reference:[5] Dixit, A.: Entry and exit decisions under uncertainty.J. Political Econ. 97 (1989), 620-638. 10.1086/261619; reference:[6] Duckworth, J. K., Zervos, M.: An investment model with entry and exit decisions.J. Appl. Probab. 37 (2000), 547-559. Zbl 0959.93058, MR 1781012, 10.1239/jap/1014842558; reference:[7] Gauthier, L., Morellec, E.: Investment under uncertainty with implementation delay. New Developments and Applications in Real Options.Available at https://infoscience.epfl.ch/record/188140/files/morellec$_-$delay.PDF (2000).; reference:[8] Isik, M., Coble, K. H., Hudson, D., House, L. O.: A model of entry-exit decisions and capacity choice under demand uncertainty.Agricultural Economics 28 (2003), 215-224. 10.1016/S0169-5150(03)00016-1; reference:[9] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus.Graduate Texts in Mathematics 113, Springer, New York (1991). Zbl 0734.60060, MR 1121940, 10.1007/978-1-4612-0949-2; reference:[10] Kjærland, F.: A real option analysis of investments in hydropower---The case of Norway.Energy Policy 35 (2007), 5901-5908. 10.1016/j.enpol.2007.07.021; reference:[11] Leung, M. K., Young, T., Fung, M. K.: The entry and exit decisions of foreign banks in Hong Kong.Manag. Decis. Econ. 29 (2008), 503-512. 10.1002/mde.1414; reference:[12] Levendorskii, S.: Perpetual American options and real options under mean-reverting processes.SSRN (2005), 27 pages. 10.2139/ssrn.714321; reference:[13] Lumley, R. R., Zervos, M.: A model for investments in the natural resource industry with switching costs.Math. Oper. Res. 26 (2001), 637-653. Zbl 1082.90537, MR 1870738, 10.1287/moor.26.4.637.10008; reference:[14] Øksendal, B.: Optimal stopping with delayed information.Stoch. Dyn. 5 (2005), 271-280. Zbl 1089.60027, MR 2147288, 10.1142/S0219493705001419; reference:[15] Øksendal, B., Sulem, A.: Applied Stochastic Control of Jump Diffusions.Universitext, Springer, Berlin (2007). Zbl 1116.93004, MR 2322248, 10.1007/978-3-540-69826-5; reference:[16] Pham, H.: Continuous-Time Stochastic Control and Optimization with Financial Applications.Stochastic Modelling and Applied Probability 61, Springer, Berlin (2009). Zbl 1165.93039, MR 2533355, 10.1007/978-3-540-89500-8; reference:[17] Pradhan, N. C., Leung, P.: Modeling entry, stay, and exit decisions of the longline fishers in Hawaii.Marine Policy 28 (2004), 311-324. 10.1016/j.marpol.2003.09.005; reference:[18] Shirakawa, H.: Evaluation of investment opportunity under entry and exit decisions.RIMS Kokyuroku 987 (1997), 107-124. Zbl 0936.91033, MR 1601586; reference:[19] Sø{d}al, S.: Entry and exit decisions based on a discount factor approach.J. Econ. Dyn. Control 30 (2006), 1963-1986. Zbl 1162.91385, MR 2273299, 10.1016/j.jedc.2005.06.011; reference:[20] Tsekrekos, A. E.: The effect of mean reversion on entry and exit decisions under uncertainty.J. Econ. Dyn. Control 34 (2010), 725-742. Zbl 1202.91340, MR 2607510, 10.1016/j.jedc.2009.10.015; reference:[21] Wang, H.: A sequential entry problem with forced exits.Math. Oper. Res. 30 (2005), 501-520. Zbl 1082.60036, MR 2142046, 10.1287/moor.1040.0141; reference:[22] Zhang, Y.: Entry and exit decisions with linear costs under uncertainty.Stochastics 87 (2015), 209-234. Zbl 1351.60052, MR 3316809, 10.1080/17442508.2014.939976

الاتاحة: http://hdl.handle.net/10338.dmlcz/147318

المؤلفون: Montes-de-Oca, Raúl, Zaitseva, Elena

مصطلحات موضوعية: keyword:discrete-time Markov process, keyword:risk-seeking expected total cost, keyword:optimal stopping rule, keyword:stability index, keyword:total variation metric, msc:60G40, msc:62L15, msc:90C40

وصف الملف: application/pdf

Relation: mr:MR3245536; zbl:Zbl 1300.60059; reference:[1] Avila-Godoy, G., Fernández-Gaucherand, E.: Controlled Markov chains with exponential risk-sensitive criteria: modularity, structured policies and applications.In: Decision and Control 1998. Proc. 37th IEEE Conference. Vol. 1, IEEE, pp. 778-783.; reference:[2] Bäuerle, N., Rieder, U.: Markov Decision Processes with Applications to Finance.Springer-Verlag, Berlin 2011. Zbl 1236.90004, MR 2808878; reference:[3] Borkar, V. S., Meyn, S. P.: Risk-sensitive optimal control for Markov decision processes with monotone cost.Math. Oper. Res. 27 (2002), 192-209. Zbl 1082.90577, MR 1886226, 10.1287/moor.27.1.192.334; reference:[4] Cavazos-Cadena, R.: Optimality equations and inequalities in a class of risk-sensitive average cost Markov decision chains.Math. Methods Oper. Res. 71 (2010), 47-84. Zbl 1189.93144, MR 2595908, 10.1007/s00186-009-0285-6; reference:[5] Cavazos-Cadena, R., Fernández-Gaucherand, E.: Controlled Markov chains with risk-sensitive criteria: Average costs, optimality equations, and optimal solutions.Math. Methods Oper. Res. 49 (1999), 299-324. MR 1687362; reference:[6] Cavazos-Cadena, R., Montes-de-Oca, R.: Optimal stationary policies in risk-sensitive dynamic programs with finite state space and nonegative rewards.Appl. Math. 27 (2000), 167-185. MR 1768711; reference:[7] Dijk, N. M. Van, Sladký, K.: Error bounds for nonnegative dynamic models.J. Optim. Theory Appl. 101 (1999), 449-474. MR 1684679, 10.1023/A:1021749829267; reference:[8] Devroye, L., Györfy, L.: Nonparametric Density Estimation: The $L_1$ View.John Wiley, New York 1986.; reference:[9] Dynkin, E. B., Yushkevich, A. A.: Controlled Markov Processes.Springer Verlag, New York 1979. MR 0554083; reference:[10] Gordienko, E. I., Yushkevich, A. A.: Stability estimates in the problem of average optimal switching of a Markov chain.Math. Methods Oper. Res. 57 (2003), 345-365. Zbl 1116.90401, MR 1990916; reference:[11] Gordienko, E. I., Lemus-Rodríguez, E., Montes-de-Oca, R.: Average cost Markov control processes: stability with respect to the Kantorovich metric.Math. Methods Oper. Res. 70 (2009), 13-33. Zbl 1176.60062, MR 2529423, 10.1007/s00186-008-0229-6; reference:[12] Gordienko, E. I., Salem, F.: Robustness inequalities for Markov control processes with unbounded costs.Syst. Control Lett. 33 (1998), 125-130. MR 1607814, 10.1016/S0167-6911(97)00077-7; reference:[13] Hernández-Lerma, O., Lasserre, J. B.: Further Topics on Discrete-time Markov Control Processes.Springer-Verlag, New York 1999. Zbl 0928.93002, MR 1697198; reference:[14] Jaśkiewicz, A.: Average optimality for risk-sensitive control with general state space.Ann. Appl. Probab. 17 (2007), 654-675. Zbl 1128.93056, MR 2308338, 10.1214/105051606000000790; reference:[15] Kartashov, N. V.: Strong Stable Markov Chains.VSP, Utrecht 1996. Zbl 0874.60082, MR 1451375; reference:[16] Marcus, S. I., Fernández-Gaucherand, E., Hernández-Hernández, D. E., Coraluppi, S., Fard, P.: Risk sensitive Markov decision processes.Progress in System and Control Theory 22 (1997), 263-280. MR 1427787; reference:[17] Masi, G. B. Di, Stettner, L.: Infinite horizon risk sensitive control of discrete time Markov processes with small risk.Systems Control Lett. 40 (2000), 15-20. Zbl 0977.93083, MR 1829070, 10.1016/S0167-6911(99)00118-8; reference:[18] Meyn, S. P., Tweedie, R. L.: Markov Chains and Stochastic Stability.Springer-Verlag, London 1993. Zbl 1165.60001, MR 1287609; reference:[19] Montes-de-Oca, R., Salem-Silva, F.: Estimates for perturbations of an average Markov decision processes with a minimal state and upper bounded stochastically ordered Markov chains.Kybernetika 41 (2005), 757-772. MR 2193864; reference:[20] Muciek, B. K.: Optimal stopping of risk processes: model with interest rates.J. Appl. Probab. 39 (2002), 261-270. MR 1908943, 10.1239/jap/1025131424; reference:[21] Shiryaev, A. N.: Optimal Stopping Rules.Springer-Verlag, New York 1978. Zbl 1138.60008, MR 2374974; reference:[22] Shiryaev, A. N.: Essential of Stochastic Finance. Facts, Models, Theory.World Scientific Publishing Co., Inc., River Edge, N. J. 1999. MR 1695318; reference:[23] Sladký, K.: Bounds on discrete dynamic programming recursions I.Kybernetika 16 (1980), 526-547. Zbl 0454.90085, MR 0607292; reference:[24] Zaitseva, E.: Stability estimating in optimal stopping problem.Kybernetika 44 (2008), 400-415. Zbl 1154.60326, MR 2436040

الاتاحة: http://hdl.handle.net/10338.dmlcz/143881

المؤلفون: Larsson, Stig, Lindberg, Carl, Warfheimer, Marcus

مصطلحات موضوعية: keyword:pairs trading, keyword:optimal stopping, keyword:Ornstein-Uhlenbeck type process, keyword:finite element method, keyword:error estimate, msc:45J05, msc:65L60, msc:65N30, msc:91G10

وصف الملف: application/pdf

Relation: mr:MR3066820; zbl:Zbl 06221230; reference:[1] Brenner, S. C., Scott, L. R.: The Mathematical Theory of Finite Element Methods. 3rd ed., Texts in Applied Mathematics 15.Springer New York (2008). MR 2373954; reference:[2] Ekström, E., Lindberg, C., Tysk, J.: Optimal liquidation of a pair trade.(to appear). MR 2792082; reference:[3] Elliott, R. J., Hoek, J. van der, Malcolm, W. P.: Pairs trading.Quant. Finance 5 (2005), 271-276. MR 2238537, 10.1080/14697680500149370; reference:[4] Evans, L. C.: Partial Differential Equations.Graduate Studies in Mathematics 19 American Mathematical Society, Providence, RI (1998). Zbl 0902.35002, MR 1625845; reference:[5] Garroni, M. G., Menaldi, J. L.: Second Order Elliptic Integro-Differential Problems.Chapman & Hall/CRC (2002). Zbl 1014.45002, MR 1911531; reference:[6] Gatev, E., Goetzmann, W., Rouwenhorst, G.: Pairs trading: performance of a relative-value arbitrage.Review of Financial Studies 19 (2006), 797-827. 10.1093/rfs/hhj020; reference:[7] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus.Graduate Texts in Mathematics 113 Springer, New York (1988). Zbl 0638.60065, MR 0917065, 10.1007/978-1-4684-0302-2_2; reference:[8] Larsson, S., Thomée, V.: Partial Differential Equations with Numerical Methods.Texts in Applied Mathematics 45 Springer, Berlin (2003). Zbl 1025.65002, MR 1995838; reference:[9] Peskir, G., Shiryaev, A.: Optimal Stopping and Free-Boundary Problems, Lectures in Mathematics, ETH Zürich.Birkhäuser Basel (2006). MR 2256030; reference:[10] Protter, P. E.: Stochastic Integration and Differential Equations.Stochastic Modelling and Applied Probability 21, Second edition. Version 2.1. Corrected third printing Springer, Berlin (2005). MR 2273672; reference:[11] Schatz, A. H.: An observation concerning Ritz-Galerkin methods with indefinite bilinear forms.Math. Comput. 28 (1974), 959-962. Zbl 0321.65059, MR 0373326, 10.1090/S0025-5718-1974-0373326-0

الاتاحة: http://hdl.handle.net/10338.dmlcz/143276

المؤلفون: Novikov, Andrey

مصطلحات موضوعية: keyword:sequential analysis, keyword:discrete-time stochastic process, keyword:dependent observations, keyword:statistical decision problem, keyword:Bayes decision, keyword:randomized stopping time, keyword:optimal stopping rule, keyword:existence and uniqueness of optimal sequential decision procedure, msc:60G40, msc:62C10, msc:62L10, msc:62L15

وصف الملف: application/pdf

Relation: mr:MR2722099; zbl:Zbl 1201.62095; reference:[1] Berger, J. O.: Statistical Decision Theory and Sequential Analysis.Second edition. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1985. MR 0804611; reference:[2] Berk, R. H.: Locally most powerful sequential tests.Ann. Statist. 3 (1975), 373–381. Zbl 0332.62063, MR 0368346, 10.1214/aos/1176343063; reference:[3] Castillo, E., García, J.: Necessary conditions for optimal truncated sequential tests.Simple hypotheses (in Spanish). Stochastica 7 (1983), 1, 63–81. MR 0766891; reference:[4] Chow, Y. S., Robbins, H., Siegmund, D.: Great Expectations: The Theory of Optimal Stopping.Houghton Mifflin Company, Boston 1971. Zbl 0233.60044, MR 0331675; reference:[5] Cochlar, J.: The optimum sequential test of a finite number of hypotheses for statistically dependent observations.Kybernetika 16 (1980), 36–47. Zbl 0434.62060, MR 0575415; reference:[6] Cochlar, J., Vrana, I.: On the optimum sequential test of two hypotheses for statistically dependent observations. Kybernetika 14 (1978), 57–69. Zbl 0376.62056, MR 0488544; reference:[7] DeGroot, M. H.: Optimal Statistical Decisions.McGraw-Hill Book Co., New York, London, Sydney 1970. Zbl 0225.62006, MR 0356303; reference:[8] Ferguson, T.: Mathematical Statistics: A Decision Theoretic Approach.Probability and Mathematical Statistics, Vol. 1. Academic Press, New York, London 1967. Zbl 0153.47602, MR 0215390; reference:[9] Ghosh, M., Mukhopadhyay, N., Sen, P. K.: Sequential Estimation.John Wiley & Sons, New York, Chichester, Weinheim, Brisbane, Singapore, Toronto 1997. Zbl 0953.62079, MR 1434065; reference:[10] Kiefer, J., Weiss, L.: Some properties of generalized sequential probability ratio tests.Ann. Math. Statist. 28 (1957), 57–75. Zbl 0079.35406, MR 0087290, 10.1214/aoms/1177707037; reference:[11] Lehmann, E. L.: Testing Statistical Hypotheses.John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London 1959. Zbl 0089.14102, MR 0107933; reference:[12] Lorden, G.: Structure of sequential tests minimizing an expected sample size. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 51 (1980), 291–302. Zbl 0407.62055, MR 0566323; reference:[13] Müller-Funk, U., Pukelsheim, F., Witting, H.: Locally most powerful tests for two-sided hypotheses. Probability and statistical decision theory, Vol. A (Bad Tatzmannsdorf 1983), pp. 31–56, Reidel, Dordrecht 1985. MR 0851017; reference:[14] Novikov, A.: Optimal sequential multiple hypothesis testing in presence of control variables.Kybernetika 45 (2009), 3, 507–528. Zbl 1165.62053, MR 2543137; reference:[15] Novikov, A.: Optimal sequential multiple hypothesis tests.Kybernetika 45 (2009), 2, 309–330. Zbl 1167.62453, MR 2518154; reference:[16] Novikov, A.: Optimal sequential procedures with Bayes decision rules.Internat. Math. Forum 5 (2010), 43, 2137–2147. Zbl 1201.62095, MR 2685120; reference:[17] Novikov, A.: Optimal sequential tests for two simple hypotheses.Sequential Analysis 28 (2009), 2, 188–217. Zbl 1162.62080, MR 2518830, 10.1080/07474940902816809; reference:[18] Novikov, A., Novikov, P.: Locally most powerful sequential tests of a simple hypothesis vs. one-sided alternatives.Journal of Statistical Planning and Inference 140 (2010), 3, 750-765. Zbl 1178.62087, MR 2558402, 10.1016/j.jspi.2009.09.004; reference:[19] Schmitz, N.: Optimal Sequentially Planned Decision Procedures.Lecture Notes in Statistics 79 (1993), New York: Springer-Verlag. Zbl 0771.62057, MR 1226454, 10.1007/978-1-4612-2736-6_4; reference:[20] Shiryayev, A. N.: Optimal Stopping Rules.Springer-Verlag, Berlin, Heidelberg, New York 1978. Zbl 0391.60002, MR 0468067; reference:[21] Wald, A.: Statistical Decision Functions.John Wiley & Sons, Inc., New York, London, Sydney 1971. Zbl 0229.62001, MR 0394957; reference:[22] Wald, A., Wolfowitz, J.: Optimum character of the sequential probability ratio test. Ann. Math. Statist. 19 (1948), 326–339. Zbl 0032.17302, MR 0026779, 10.1214/aoms/1177730197; reference:[23] Weiss, L.: On sequential tests which minimize the maximum expected sample size. J. Amer. Statist. Assoc. 57 (1962), 551–566. Zbl 0114.10304, MR 0145630, 10.1080/01621459.1962.10500543; reference:[24] Zacks, S.: The Theory of Statistical Inference.Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, London, Sydney 1971. MR 0420923

الاتاحة: http://hdl.handle.net/10338.dmlcz/140782

المؤلفون: Novikov, Andrey

مصطلحات موضوعية: keyword:sequential analysis, keyword:sequential hypothesis testing, keyword:multiple hypotheses, keyword:control variable, keyword:independent observations, keyword:optimal stopping, keyword:optimal control, keyword:optimal decision, keyword:optimal sequential testing procedure, keyword:Bayes, keyword:sequential probability ratio test, msc:60G40, msc:62C99, msc:62L10, msc:62L15, msc:93E20

وصف الملف: application/pdf

Relation: mr:MR2543137; zbl:Zbl 1165.62053; reference:[1] N. Cressie and P. B. Morgan: The VRPT: A sequential testing procedure dominating the SPRT.Econometric Theory 9 (1993), 431–450. MR 1241983; reference:[2] M. Ghosh, N. Mukhopadhyay, and P. K. Sen: Sequential Estimation.John Wiley, New York – Chichester – Weinheim – Brisbane – Singapore – Toronto 1997. MR 1434065; reference:[3] G. W. Haggstrom: Optimal stopping and experimental design.Ann. Math. Statist. 37 (1966), 7–29. Zbl 0202.49201, MR 0195221; reference:[4] G. Lorden: Structure of sequential tests minimizing an expected sample size.Z. Wahrsch. verw. Geb. 51 (1980), 291–302. Zbl 0407.62055, MR 0566323; reference:[5] M. B. Malyutov: Lower bounds for the mean length of a sequentially planned experiment.Soviet Math. (Iz. VUZ) 27 (1983), 11, 21–47. MR 0733570; reference:[6] A. Novikov: Optimal sequential testing of two simple hypotheses in presence of control variables.Internat. Math. Forum 3 (2008), 41, 2025–2048. Preprint arXiv:0812.1395v1 [math.ST] (http://arxiv.org/abs/0812.1395) MR 2470661; reference:[7] A. Novikov: Optimal sequential multiple hypothesis tests.Kybernetika 45 (2009), 2, 309–330. Zbl 1167.62453, MR 2518154; reference:[8] A. Novikov: Optimal sequential procedures with Bayes decision rules.Preprint arXiv:0812.0159v1 [math.ST]( http://arxiv.org/abs/0812.0159) MR 2685120; reference:[9] A. Novikov: Optimal sequential tests for two simple hypotheses based on independent observations.Internat. J. Pure Appl. Math. 45 (2008), 2, 291–314. MR 2421867; reference:[10] N. Schmitz: Optimal Sequentially Planned Decision Procedures.(Lecture Notes in Statistics 79.) Springer-Verlag, New York 1993. Zbl 0771.62057, MR 1226454; reference:[11] I. N. Volodin: Guaranteed statistical inference procedures (determination of the optimal sample size).J. Math. Sci. 44 (1989), 5, 568–600. Zbl 0666.62077, MR 0885413; reference:[12] A. Wald and J. Wolfowitz: Optimum character of the sequential probability ratio test.Ann. Math. Statist. 19 (1948), 326–339. MR 0026779; reference:[13] S. Zacks: The Theory of Statistical Inference.John Wiley, New York – London – Sydney – Toronto 1971. Zbl 0321.62003, MR 0420923

الاتاحة: http://hdl.handle.net/10338.dmlcz/140020

المؤلفون: Gordienko, Evgueni, Novikov, Andrey, Zaitseva, Elena

مصطلحات موضوعية: keyword:sequential hypotheses test, keyword:simple hypothesis, keyword:optimal stopping, keyword:sequential probability ratio test, keyword:likelihood ratio statistic, keyword:stability inequality, msc:62L10, msc:62L15

وصف الملف: application/pdf

Relation: mr:MR2518155; zbl:Zbl 1165.62052; reference:[1] Y. S. Chow, H. Robbins, and D. Siegmund: Great Expectations: The Theory of Optimal Stopping.Houghton Mifflin Company, Boston 1971. MR 0331675; reference:[2] E. I. Gordienko and F. S. Salem: Estimates of stability of Markov control processes with unbounded costs.Kybernetika 36 (2000), 195–210. MR 1760024; reference:[3] E. I. Gordienko and A. A. Yushkevich: Stability estimates in the problem of average optimal switching of a Markov chain.Math. Methods Oper. Res. 57 (2003), 345–365. MR 1990916; reference:[4] P. J. Huber: A robust version of the probability ratio test.Ann. Math. Statist. 36 (1965), 1753–1758. Zbl 0137.12702, MR 0185747; reference:[5] A. Kharin: On robustifying of the sequential probability ratio test for a discrete model under “contaminations".Austrian J. Statist. 3 (2002), 4, 267–277.; reference:[6] A. Kharin: Robust sequential testing of hypotheses on discrete probability distributions.Austrian J. Statist. 34 (2005), 2, 153–162.; reference:[7] G. Lorden: Structure of sequential tests minimizing an expected sample size.Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. Zbl 0407.62055, MR 0566323; reference:[8] V. Mackevičius: Passage to the limit in problems of optimal stopping of Markov processes (in Russian).Litovsk. Mat. Sb. (Russian) 13 (1973), 1, 115–128, 236. MR 0347017; reference:[9] R. Montes-de-Oca, A. Sakhanenko, and F. Salem-Silva: Estimates for perturbations of general discounted Markov control chains.Appl. Math. 30 (2003), 287–304. MR 2029538; reference:[10] A. Novikov: Optimal sequential tests for two simple hypotheses.Sequential Analysis 28 (2009), No. 2. Zbl 1162.62080, MR 2518830; reference:[11] A. Novikov: Optimal sequential tests for two simple hypotheses based on independent observations.Internat. J. Pure Appl. Math. 45 (2008), 2, 291–314. MR 2421867; reference:[12] V. V. Petrov: Sums of Independent Random Variables.Springer, New York 1975. Zbl 1125.60024, MR 0388499; reference:[13] P. X. Quang: Robust sequential testing.Ann. Statist. 13 (1985), 638–649. Zbl 0588.62136, MR 0790562; reference:[14] A. N. Shiryayev: Statistical Sequential Analysis.Nauka, Moscow 1969. (In Russian.); reference:[15] A. Wald and J. Wolfowitz: Optimum character of the sequential probability ratio test.Ann. Math. Statist. 19 (1948), 326–339. MR 0026779; reference:[16] J. Whitehead: The Design and Analysis of Sequential Clinical Trials.Wiley, New York 1997. Zbl 0747.62109, MR 0793018

الاتاحة: http://hdl.handle.net/10338.dmlcz/140072

المؤلفون: Zaitseva, Elena

مصطلحات موضوعية: keyword:discrete-time Markov process, keyword:optimal stopping rule, keyword:stability index, keyword:total variation metric, keyword:contractive operator, keyword:optimal asset selling, msc:60G40, msc:60J10

وصف الملف: application/pdf

Relation: mr:MR2436040; zbl:Zbl 1154.60326; reference:[1] Allart P.: Optimal stopping rules for correlated random walks with a discount.J. Appl. Prob. 41 (2004), 483–496 MR 2052586; reference:[2] Bertsekas D. P.: Dynamic Programming: Deterministic and Stochastic Models.Prentice Hall, Englewood Cliffs, N. J. 1987 Zbl 0649.93001, MR 0896902; reference:[3] Bertsekas D. P., Shreve S. E.: Stochastic Optimal Control: The Discrete Time Case.Academic Press, New York 1979 Zbl 0633.93001, MR 0511544; reference:[4] Dijk N. M. Van: Perturbation theory for unbounded Markov reward process with applications to queueing systems.Adv. in Appl. Probab. 20 (1988), 99–111 MR 0932536; reference:[5] Dijk N. M. Van, Sladký K.: Error bounds for nonnegative dynamic models.J. Optim. Theory Appl. 101 (1999), 449–474 MR 1684679; reference:[6] Dynkin E. B., Yushkevich A. A.: Controlled Markov Process.Springer-Verlag, New York 1979 MR 0554083; reference:[7] Favero G., Runggaldier W. J.: A robustness results for stochastic control.Systems Control Lett. 46 (2002), 91–97 MR 2010062; reference:[8] Gordienko E. I.: An estimate of the stability of optimal control of certain stochastic and deterministic systems.J. Soviet Math. 59 (1992), 891–899. (Translated from the Russian publication of 1989) MR 1163393; reference:[9] Gordienko E. I., Salem F. S.: Robustness inequality for Markov control process with unbounded costs.Systems Control Lett. 33 (1998), 125–130 MR 1607814; reference:[10] Gordienko E. I., Yushkevich A. A.: Stability estimates in the problem of average optimal switching of a Markov chain.Math. Methods Oper. Res. 57 (2003), 345–365 Zbl 1116.90401, MR 1990916; reference:[11] Gordienko E. I., Lemus-Rodríguez E., Montes-de-Oca R.: Discounted cost optimality problem: stability with respect to weak metrics.In press in: Math. Methhods Oper. Res. (2008) Zbl 1166.60041, MR 2429561; reference:[12] Hernández-Lerma O., Lassere J. B.: Discrete-Time Markov Control Processes: Basic Optimality Criteria.Springer-Verlag, N.Y. 1996; reference:[13] Jensen U.: An optimal stopping problem in risk theory.Scand. Actuarial J.2 (1997), 149–159 Zbl 0888.62104, MR 1492423; reference:[14] Meyn S. P., Tweedie R. L.: Markov Chains and Stochastic Stability.Springer-Verlag, London 1993 Zbl 1165.60001, MR 1287609; reference:[15] Montes-de-Oca R., Salem-Silva F.: Estimates for perturbations of an average Markov decision process with a minimal state and upper bounded by stochastically ordered Markov chains.Kybernetika 41 (2005), 757–772 MR 2193864; reference:[16] Montes-de-Oca R., Sakhanenko, A., Salem-Silva F.: Estimate for perturbations of general discounted Markov control chains.Appl. Math. 30 (2003), 287–304 MR 2029538; reference:[17] Muciek B. K.: Optimal stopping of a risk process: model with interest rates.J. Appl. Prob. 39 (2002), 261–270 Zbl 1011.62111, MR 1908943; reference:[18] Müller A.: How does the value function of a Markov decision process depend on the transition probabilities? Math.Oper. Res. 22 (1997), 872–885 MR 1484687; reference:[19] Schäl M.: Conditions for optimality in dynamic programming and for the limit of $n$-stage optimal policies to be optimal.Z. Wahrsch. verw. Gebiete 32 (1975), 179–196 Zbl 0316.90080, MR 0378841; reference:[20] Shiryaev A. N.: Optimal Stopping Rules.Springer-Verlag, New York 1978 Zbl 1138.60008, MR 2374974; reference:[21] Shiryaev A. N.: Essential of Stochastic Finance.Facts, Models, Theory. World Scientific Publishing Co., Inc., River Edge, N.J. 1999 MR 1695318

الاتاحة: http://hdl.handle.net/10338.dmlcz/135859