المؤلفون: Martínez Sánchez, Jaime, Zaitseva, Elena

مصطلحات موضوعية: keyword:discrete-time Markov control processes, keyword:average criterion, keyword:stability index, keyword:Prokhorov metric, msc:90C40, msc:93E20

وصف الملف: application/pdf

Relation: mr:MR3423190; zbl:Zbl 06537775; reference:[1] Arapostathis, A., Borkar, V. S., Fernández-Gaucherand, E., Ghosh, M. K., Marcus, S. I.: Discrete-time controlled Markov processes with average cost criterion: A survey.SIAM J. Control and Optimization 31 (1993), 282-344. Zbl 0770.93064, MR 1205981, 10.1137/0331018; reference:[2] Dudley, R. M.: Real Analysis and Probability.Wadsworth and Brooks/Cole, Pacific Grove 1989. Zbl 1023.60001, MR 0982264, 10.1017/s0013091500018265; reference:[3] Dudley, R. M.: The speed of mean Glivenko-Cantelly convergence.Ann. Math. Stat. 40 (1969), 40-50. MR 0236977, 10.1214/aoms/1177697802; reference:[4] Dynkin, E. B., Yushkevich, A. A.: Controlled Markov Processes.Springer-Verlag, New York 1979. MR 0554083, 10.1002/zamm.19810610317; reference:[5] Gordienko, E., 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:[6] Gordienko, E. I.: Stability estimates for controlled Markov chains with a minorant.J. Soviet. Math. 40 (1988), 481-486. Zbl 0638.90101, MR 0957101, 10.1007/bf01083641; reference:[7] 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:[8] Hernández-Lerma, O.: Adaptive Markov Control Processes.Springer-Verlag, New York 1989. Zbl 0677.93073, MR 0995463, 10.1007/978-1-4419-8714-3; reference:[9] Montes-de-Oca, R., Salem-Silva, F.: Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains.Kybernetika 41 (2005), 757-772. Zbl 1249.90313, MR 2193864; reference:[10] Rachev, S. T., Rüschendorf, L.: Mass Transportation Problem, Vol. II: Applications.Springer, New York 1998. MR 1619171; reference:[11] Vega-Amaya, O.: The average cost optimality equation: a fixed point approach.Bol. Soc. Math. Mexicana 9 (2003), 185-195. Zbl 1176.90626, MR 1988598

الاتاحة: http://hdl.handle.net/10338.dmlcz/144471

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: 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