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Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…

In this article, the notion of viscosity solution is introduced for the path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with the optimal control problems for path-dependent stochastic differential equations. We identify…

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…

In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…

We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…

This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…

We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. At the PDE level, PI is fundamentally…

We introduce a price impact model which accounts for finite market depth, tightness and resilience. Its coupled bid- and ask-price dynamics induce convex liquidity costs. We provide existence of an optimal solution to the classical problem…

We study the stochastic control-stopping problem when the data are of polynomial growth. The approach is based on backward stochastic dierential equations (BSDEs for short). The problem turns into the study of a specic reected BSDE with a…

We study an infinite-horizon optimal investment, consumption and insurance problem for an economic agent who consumes a perishable and a durable good. The agent trades in a risk-free asset, a risky asset, and a durable good whose price…

In this article, we study optimal investment and consumption in an incomplete stochastic factor model for a power utility investor on the infinite horizon. When the state space of the stochastic factor is finite, we give a complete…

We consider a two-dimensional optimal dividend problem in the context of two branches of an insurance company with compound Poisson surplus processes dividing claims and premia in some specified proportions. We solve the stochastic control…

This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset…

In this work we study the stochastic recursive control problem, in which the aggregator (or called generator) of the backward stochastic differential equation describing the running cost is continuous but not necessarily Lipschitz with…

The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a…

In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…

In this paper, we study a kind of optimal control problem for forward-backward stochastic differential equations (FBSDEs for short) of McKean--Vlasov type via the dynamic programming principle (DPP for short) motivated by studying the…

We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop…

Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…