Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching

Paul Gassiat, Fausto Gozzi, and Huyên Pham. "Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching." Banach Center Publications 105.1 (2015): 103-118. <http://eudml.org/doc/286505>.

@article{PaulGassiat2015,
abstract = {We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption under a non-bankruptcy constraint. In this paper we perform the first step needed to treat this model: the proof of the dynamic programming principle (DPP) and the characterization of the value function as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. This puts the basis for the analysis of the optimal solution of the model which is done in the companion paper of the authors (SIAM J. Control. Optim. 52 (2014)). The proof of the dynamic programming principle is not standard as in this case we do not know a priori if the value function is continuous up to the boundary.},
author = {Paul Gassiat, Fausto Gozzi, Huyên Pham},
journal = {Banach Center Publications},
keywords = {dynamic programming; investment/consumption problem; illiquid markets; continuous-time Markov chain; Hamilton-Jacobi-Bellman equation; viscosity solution},
language = {eng},
number = {1},
pages = {103-118},
title = {Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching},
url = {http://eudml.org/doc/286505},
volume = {105},
year = {2015},
}

TY - JOUR
AU - Paul Gassiat
AU - Fausto Gozzi
AU - Huyên Pham
TI - Dynamic programming for an investment/consumption problem in illiquid markets with regime-switching
JO - Banach Center Publications
PY - 2015
VL - 105
IS - 1
SP - 103
EP - 118
AB - We consider an illiquid financial market with different regimes modeled by a continuous time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the market regime. Moreover, the risky asset price is subject to liquidity shocks, which change its rate of return and volatility, and induce jumps on its dynamics. In this setting, we study the problem of an economic agent optimizing her expected utility from consumption under a non-bankruptcy constraint. In this paper we perform the first step needed to treat this model: the proof of the dynamic programming principle (DPP) and the characterization of the value function as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equation. This puts the basis for the analysis of the optimal solution of the model which is done in the companion paper of the authors (SIAM J. Control. Optim. 52 (2014)). The proof of the dynamic programming principle is not standard as in this case we do not know a priori if the value function is continuous up to the boundary.
LA - eng
KW - dynamic programming; investment/consumption problem; illiquid markets; continuous-time Markov chain; Hamilton-Jacobi-Bellman equation; viscosity solution
UR - http://eudml.org/doc/286505
ER -