共查询到20条相似文献,搜索用时 15 毫秒
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An error in the proof of Theorem 4.1 of Ref. 1 is corrected. 相似文献
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Lijun Bo Chenggui Yuan 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(6):841-863
In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to equation, we prove that the Markov semigroup generated by the segment process corresponding to the solution admits a unique invariant measure on the Skorohod space when the coefficients of equation satisfy a class of monotone conditions. Finally, we establish a relationship between the regulator and the local time of the solution and discuss a local time property at large time under the stationary setting. 相似文献
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On the Isaacs equation of differential games of fixed duration 总被引:1,自引:0,他引:1
J. Yong 《Journal of Optimization Theory and Applications》1986,50(2):359-364
The conditions under which the value function of fixed-duration differential games satisfies the Isaacs equation are relaxed.The author thanks Professor L. D. Berkovitz for posing the problem. 相似文献
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This paper investigates a class of reinsurance game problems between two insurance companies under the framework of non-zero-sum stochastic differential games. Both insurers can purchase proportional reinsurance contracts from reinsurance markets and have the option of conducting capital injections. We assume the reinsurance premium is calculated under the generalized variance premium principle. The objective of each insurer is to maximize the expected value that synthesizes the discounted utility of his surplus relative to a reference point, the penalties caused by his own capital injection interventions, and the gains brought by capital injections of his competitor. We prove the verification theorem and derive explicit expressions of the Nash equilibrium strategy by solving the corresponding quasi-variational inequalities. Numerical examples are also conducted to illustrate our results. 相似文献
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Antoni Leon Dawidowicz Najemedin Haribash Anna Poskrobko 《Mathematical Methods in the Applied Sciences》2007,30(7):779-787
The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Bonnans J. Frederic; Maroso Stefania; Zidani Housnaa 《IMA Journal of Numerical Analysis》2006,26(1):188-212
** Email: frederic.bonnans{at}inria.fr*** Email: stefania.maroso{at}inria.fr**** Email: zidani{at}ensta.fr We obtain error bounds for monotone approximation schemes ofa particular Isaacs equation. This is an extension of the theoryfor estimating errors for the HamiltonJacobiBellmanequation. To obtain the upper error bound, we consider the Krylovregularization of the Isaacs equation to build an approximatesub-solution of the scheme. To get the lower error bound, weextend the method of Barles & Jakobsen (2005, SIAM J. Numer.Anal.) which consists in introducing a switching system whosesolutions are local super-solutions of the Isaacs equation. 相似文献
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Interactive economic dynamics and differential games 总被引:2,自引:0,他引:2
This survey reviews the applications of differential game theory in analyzing issues in the economic literature. The needs of the economic discipline are juxtaposed with the merits of various existing types of differential games. Suggestions are also made as to areas holding great promise for future research.The authors are grateful to Prof. George Leitmann for suggestions to their final draft, which improved the clarity of certain assumptions in keeping with the literature. 相似文献
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Rainer BUCKDAHN 《应用数学学报(英文版)》2011,27(4):647-678
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory
of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for
the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward
way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper
and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. The method differs significantly from
those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove
a new estimate for RBSDEs being sharper than that in the paper of El Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997),
which turns out to be very useful because it allows us to estimate the L
p
-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution
to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs
equation with obstacle. 相似文献
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Abstract
This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states. It focuses
on both unscaled and scaled occupation measures. Under mild conditions, a mean-square estimate is obtained. By averaging the
fast components, we obtain an aggregated process. Although the aggregated process itself may be non-Markovian, its weak limit
is a Markov chain with much smaller state space. Moreover, a suitably scaled sequence consisting of a component of scaled
occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching
diffusion component.
* The research of this author is supported in part by the National Science Foundation under Grant DMS-9877090
** The research of this author is supported in part by the Office of Naval Research Grant N00014-96-1-0263
*** The research of this author is supported in part by Wayne State University 相似文献
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We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.The authors wish to thank Prof. T. Parthasarathy for pointing out an error in an earlier version of this paper. M. K. Ghosh wishes to thank Prof. A. Arapostathis and Prof. S. I. Marcus for their hospitality and support. 相似文献
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This paper investigates the impact of relative performance concerns on the longevity risk transfer market. When an insurer concerns about the relative performance in a two-insurer economy, she maximizes the expected utility of her terminal wealth benchmarked against her competitor’s. The problem formulation for a general utility, a general interest rate process and cointegrated mortality rates uses a nonzero sum stochastic differential game approach. Explicit solution of the Nash equilibrium is derived for constant relative risk adverse insurers under the Vasicek-type stochastic interest and mortality rates. Existence and uniqueness of the Nash equilibrium are established for the CIR-type models, which rule out negative interest and mortality rates. While previous studies based on the single-agent approaches have shown a high investment demand in longevity bonds, the launch of it was unsuccessful in reality. Ours supplements that the demand is much lower subject to the relative performance concerns. 相似文献
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Bapurao C. Dhage 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e319
In this paper, an existence result for perturbed abstract measure differential equations is proved via hybrid fixed point theorems of Dhage [B.C. Dhage, On some nonlinear alternatives of Leray-Schauder type and functional integral equations, Arch. Math. (Brno) 42 (2006) 11-23] under the mixed generalized Lipschitz and Carathéodory conditions. The existence of the extremal solutions is also proved under certain monotonicity conditions and using a hybrid fixed point theorem of Dhage given in the above-mentioned reference, on ordered Banach spaces. Our existence results include the existence results of Sharma [R.R. Sharma, An abstract measure differential equation, Proc. Amer. Math. Soc. 32 (1972) 503-510], Joshi [S.R. Joshi, A system of abstract measure delay differential equations, J. Math. Phy. Sci. 13 (1979) 497-506] and Shendge and Joshi [G.R. Shendge, S.R. Joshi, Abstract measure differential inequalities and applications, Acta Math. Hung. 41 (1983) 53-54] as special cases under weaker continuity condition. 相似文献
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The paper presents a stochastic differential game model of a common-property commercial fishery and determines a feedback Nash equilibrium of the game. Closed-form expressions for the value functions, the equilibrium harvesting strategies, and stationary distributions of the fish stock are derived. Sensitivity analyses with respect tot he model parameters are carried out. The paper also considers equilibrium outcomes under joint maximization and surplus maximization. In the latter case, an optimal market size (i.e., number of firms) is identified.The research of the first author was supported in part by Grant 5.20.31.02 from the Danish Research Council for the Social Sciences. The research of the second author was supported in part by the CRGC Fund of the University of Hong Kong. The authors would like to thank the editor for constructive comments. 相似文献