Stochastic Functional Differential Equation under Regime Switching
نویسندگان
چکیده
We discuss stochastic functional differential equation under regime switching dx t f xt, r t , t dt q r t x t dW1 t σ r t |x t |βx t dW2 t . We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially stable of this system.
منابع مشابه
General Equilibrium Asset Pricing under Regime Switching
We have investigated the asset pricing problem in a general equilibrium in an economy with two states. Based on the assumption of a CRRA utility function, we have derived a partial differential equation satisfied by the representative agent’s cost function. In the case when the representative agent doesn’t have intermediate consumption, we have found an explicit solution of the cost function. A...
متن کاملAsymptotic properties of consensus-type algorithms for networked systems with regime-switching topologies
This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate paramet...
متن کاملThe Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching
Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochas...
متن کاملOn risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy
Résumé/Abstract: We consider a risk minimization problem in a continuous-time Markovian regimeswitching financial model modulated by a continuous-time, observable and finitestate Markov chain whose states represent different market regimes. We adopt a particular form of convex risk measure, which includes the entropic risk measure as a particular case, as a proxy of risk. The riskminimization p...
متن کاملMethods for Pricing American Options under Regime Switching
We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical...
متن کامل