Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market

Date

2020-08-01

Author

Savku, E.
Weber, Gerhard Wilhelm

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

392
views

0
downloads

We apply dynamic programming principle to discuss two optimal investment problems by using zero-sum and nonzero-sum stochastic game approaches in a continuous-time Markov regime-switching environment within the frame work of behavioral finance. We represent different states of an economy and, consequently, investors' floating levels of psychological reactions by aD-state Markov chain. The first application is a zero-sum game between an investor and the market, and the second one formulates a nonzero-sum stochastic differential portfolio game as the sensitivity of two investors' terminal gains. We derive regime-switching Hamilton-Jacobi-Bellman-Isaacs equations and obtain explicit optimal portfolio strategies with Feynman-Kac representations of value functions. We illustrate our results in a two-state special case and observe the impact of regime switches by comparative results.

Subject Keywords

Management Science and Operations Research, General Decision Sciences

URI

https://hdl.handle.net/11511/51595

Journal

ANNALS OF OPERATIONS RESEARCH

DOI

https://doi.org/10.1007/s10479-020-03768-5

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS Kalayci, Betul; Ozmen, Ayse; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01) Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on s...
Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs Alp, O; Erkip, NK; Gullu, R (Institute for Operations Research and the Management Sciences (INFORMS), 2003-01-01) We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the ...
Anti-periodic solutions for state-dependent impulsive recurrent neural networks with time-varying and continuously distributed delays Sayli, Mustafa; YILMAZ, ENES (Springer Science and Business Media LLC, 2017-11-01) In this paper, we address a new model of neural networks related to the impulsive phenomena which is called state-dependent impulsive recurrent neural networks with time-varying and continuously distributed delays. We investigate sufficient conditions on the existence and uniqueness of exponentially stable anti-periodic solution for these neural networks by employing method of coincide degree theory and an appropriate Lyapunov function. Moreover, we present an illustrative example to show the effectiveness ...
Neural network calibrated stochastic processes: forecasting financial assets Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01) If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
Assessment of criteria - rich rankings for environmental policy making Yeralan, Sencer; Ozdoglar, Mehmet Rasit; Azizoğlu, Meral (Inderscience Publishers, 2011-12-01) This paper illustrates the use of mathematical programming techniques to extract more information out of composite indexes (e.g., the EPI-2008) that would assist decision makers. While recognising the qualitative aspects of such decision making, in order to support and guide the policy making process, we develop analytical tools to assist the process. We carefully delineate our models to be limited only to the provable quantitative properties of the available objective data. However, such data are processed...

Citation Formats

E. Savku and G. W. Weber, “Stochastic differential games for optimal investment problems in a Markov regime-switching jump-diffusion market,” ANNALS OF OPERATIONS RESEARCH, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51595.