Related papers: Time-consistent investment and consumption strateg…
This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is…
This paper examines a continuous time intertemporal consumption and portfolio choice problem with a stochastic differential utility preference of Epstein-Zin type for a robust investor, who worries about model misspecification and seeks…
In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
When we implement a portfolio selection methodology under a mean-risk formulation, it is essential to correctly model investors' risk aversion which may be time-dependent, or even state-dependent during the investment procedure. In this…
We study equilibrium feedback strategies for a family of dynamic mean-variance problems with competition among a large group of agents. We assume that the time horizon is random and each agent's risk aversion depends dynamically on the…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
This paper studies the mean-field Markov decision process (MDP) with the centralized stopping under the non-exponential discount. The problem differs fundamentally from most existing studies on mean-field optimal control/stopping due to its…
In this paper, we study a mean-variance optimization problem in an infinite horizon discrete time discounted Markov decision process (MDP). The objective is to minimize the variance of system rewards with the constraint of mean performance.…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
The Merton investment-consumption problem is fundamental, both in the field of finance, and in stochastic control. An important extension of the problem adds transaction costs, which is highly relevant from a financial perspective but also…
We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the…
Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new…
The Merton problem is the well-known stochastic control problem of choosing consumption over time, as well as an investment mix, to maximize expected constant relative risk aversion (CRRA) utility of consumption. Merton formulated the…
The paper studies problem of continuous time optimal portfolio selection for a incom- plete market diffusion model. It is shown that, under some mild conditions, near optimal strategies for investors with different performance criteria can…
For time inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by the sophisticated agents. In this short note we construct a deterministic continuous time example where the unique equilibrium is…
We revisit the classical Merton consumption--investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $\alpha$-integral, interpolating between It\^{o}, Stratonovich, and…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem…
We introduce an infinite-horizon, continuous-time portfolio selection problem faced by an agent with periodic S-shaped preference and present bias. The inclusion of a quasi-hyperbolic discount function leads to time-inconsistency and we…