Stochastic Control & Optimal Stopping

This paper is concerned with a long standing optimal dividend payout problem subject to the so-called ratcheting constraint, that is, the dividend payout rate shall be non-decreasing over time and is thus self-path-dependent. The surplus process is modeled by a drifted Brownian motion process and th

In this work we consider the exponential utility maximization problem in the framework of semistatic hedging.

This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, u

We consider a mean-field model of firms competing à la Cournot on a commodity market, where the commodity price is given in terms of a power inverse demand function of the industry-aggregate production. Investment is irreversible and production capacity depreciates at a constant rate. Production is

This paper studies Merton’s problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a tracking formulation where the fund manager aims to maximize the trade-off between the expected utility of consumption and the expected largest shortfall of the

We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state space, continuous-time, and finite-horizon. The value funct

We give sufficient conditions ensuring that, at every fixed positive time, the scalar backward component of a Markovian forward-backward stochastic differential equation with multidimensional forward process admits a density with respect to Lebesgue measure. Existing density criteria for BSDEs often

We consider the distribution-constrained optimal stopping problem $\sup_{τ\sim μ} \mathbb E[B^τ]$, where $μ$ is a probability distribution on $\mathbb R+$, and $(B^_t)$ denotes the running maximum of a standard Brownian motion. This problem was introduced in Beiglbock et al. (PTRF, 2018), where

We study the infinite-horizon optimal investment and consumption problem in a general class of continuous financial markets, where uncertainty is driven by a continuous non-decreasing stochastic clock representing accumulated variance. This framework encompasses classical Markovian and non-Markovian

We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the $G$-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic $G$-BSDE for the logarithmic price. Under suita

Liquidation of collateral are the primary safeguard for solvency of lending protocols in decentralized finance. However, the mechanics of liquidations expose these protocols to predatory price manipulations and other forms of Maximal Extractable Value (MEV). In this paper, we characterize the optima

We study a goal-based portfolio selection problem in which an investor aims to meet multiple financial goals, each with a specific deadline and target amount. Trading the stock incurs a strictly positive transaction cost. Using the stochastic Perron’s method, we show that the value function is the u

This paper introduces a semi-analytical method for pricing American options on assets (stocks, ETFs) that pay discrete and/or continuous dividends. The problem is notoriously complex because discrete dividends create abrupt price drops and affect the optimal exercise timing, making traditional conti

Investment herding, a phenomenon where households mimic the decisions of others rather than relying on their own analysis, has significant effects on financial markets and household behavior. Excessive investment herding may reduce investments and lead to a depletion of household consumption, which

This paper investigates optimal withdrawal strategies and behavior of policyholders in a variable annuity (VA) contract with a guaranteed minimum withdrawal benefit (GMWB) rider incorporating taxation and a ratchet mechanism for enhancing the benefit base during the life of the contract. Mathematica

We give a criterion under which the expected return on a ticket for certain large lotteries is positive. In this circumstance, we use elementary portfolio analysis to show that an optimal investment strategy includes a very small allocation for such tickets.

We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding stochastic calculus by establishing representation theorems for ex

We model the trading activity between a broker and her clients (informed and uninformed traders) as an infinite-horizon stochastic control problem. We derive the broker’s optimal dealing strategy in closed form and use this to introduce an algorithm that bypasses the need to calibrate individual par

This paper is devoted to time-consistent control problems of portfolio selection with strictly monotone mean-variance preferences. These preferences are variational modifications of the conventional mean-variance preferences, and remain time-inconsistent as in mean-variance optimization problems. To

This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon, featu