Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model

Abstract

We prove a sufficient stochastic maximum principle for the optimal control of a regimeswitching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem. . where b n : [0, T ]×R N ×R P ×I → R and σ nm : [0, T ]×R N ×R P ×I → R are given continuous functions for n, m = 1, . . . , N . Using A ⊤ to denote the transpose of a matrix A, set b(t) := (b 1 (t), . . . , b N (t)) ⊤ and σ(t) := (σ nm (t)) N n,m=1 . We consider a performance criterion defined for each x ∈ R N asf (t, X(t), u(t), α(t)) dt + h(X(T ), α(T )) X(0) = x, α(0) = i 0 ,

Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models

“…Example 4.5. (Quadratic Loss Minimization) Here we adopt the setting in [12,Section 6]. Let (Ω, F, {F t } 0≤t≤T , P) be a complete probability space on which defined a 1-dimensional standard Brownian motion W and a continuous time Markov chain α valued in a finite state space I = {1, · · · d} with generator matrix Q = [q ij ] i,j∈I and initial mode α(0) = i 0 .…”

Equilibrium strategies for time-inconsistent stochastic switching systems

“…See [41] and references cited therein for a detailed presentation. The readers are also referred to [37,5,6,47,16] for some results relevant to financial applications with regime-switching systems.…”

A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

“…Stochastic control problem for Markovian regime-switching model has received a lot of attention recently; See e.g., [4,5,13,14,19,21]. Each state of the Markov chain represents a state of an economy.…”