This hub holds the mathematical engine room of quantitative finance: stochastic control (choose a policy that steers a diffusion), optimal stopping (choose a time to act), and the machinery that solves them — Hamilton–Jacobi–Bellman equations, viscosity solutions, backward stochastic differential equations, and mean-field games for the many-player limit. The classic applications are Merton-style consumption and investment, optimal liquidation, dividend and reinsurance control, and American-option exercise.
Most papers here are Lab Rats by our scoring: deep theory, little or no data. That is not a criticism of the work, but it changes how you read it. The questions that matter are whether the model’s state variables are observable in practice, whether the closed-form or numerical solution degrades gracefully when parameters are estimated rather than known, and whether a paper that claims a strategy ever confronts it with transaction costs or discrete rebalancing. The handful of papers that pair a control result with a calibrated numerical study rank highest below.
Related hubs: Options & Derivatives, Portfolio Optimization, HFT & Optimal Execution, Insurance & Actuarial Risk.
This paper considers an insurer with two collaborating business lines that faces three critical decisions: (1) dividend payout, (2) reinsurance coverage, and (3) capital injection between the lines, in the presence of model uncertainty. The insurer considers the reference model to be an approximatio
In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg model, the stochastic factor represents the expected excess re
This paper bridges reinforcement learning (RL) and risk-sensitive stochastic control by introducing a tractable exploration mechanism for policy search in risk-sensitive portfolio management, with known and unknown model parameters, that yields an endogenous relative-entropy regularization. We const
Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we propose a fully probabilistic framework based on the Doob-Meyer-
Achieving net-zero carbon emissions requires a transformation of energy systems, industrial processes, and consumption patterns. In particular, a transition towards that goal involves a gradual reduction of excess carbon emissions that are not essential for the well-functioning of society. In this p
This paper considers an insurer with two collaborating business lines that must make three critical decisions: (1) dividend payout, (2) a combination of proportional and excess-of-loss reinsurance coverage, and (3) capital injection between the lines. The reserve level of each line is modeled using
We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in their dividend distribution, and the mean-variance (MV) criter
This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer’s surplus follows the diffusion approximation of the Cramér-Lundberg model, and the insurer can purchase prop
This paper addresses the problem of determining the optimal time for an individual to convert retirement savings into a lifetime annuity. The individual invests their wealth into a dividend-paying fund that follows the dynamics of a geometric Brownian motion, exposing them to market risk. At the sam
This paper presents a derivation of the explicit price for the perpetual American put option time-capped by the first drawdown epoch beyond a predefined level. We consider the market in which an asset price is described by geometric Lévy process with downward exponential jumps. We show that the opti
This paper considers an insurer with two collaborating business lines, and the risk exposure of each line follows a diffusion risk model. The manager of the insurer makes three decisions for each line: (i) dividend payout, (ii) (proportional) reinsurance coverage, and (iii) capital injection (from o
We investigate the full dynamics of capital allocation and wealth distribution of heterogeneous agents in a frictional economy during booms and busts using tools from mean-field games. Two groups in our models, namely the expert and the household, are interconnected within and between their classes
This paper investigates the dynamic reinsurance design problem under the mean-variance criterion, incorporating heterogeneous beliefs between the insurer and the reinsurer, and introducing an incentive compatibility constraint to address moral hazard. The insurer’s surplus process is modeled using t
In financial markets, agents often mutually influence each other’s investment strategies and adjust their strategies to align with others. However, there is limited quantitative study of agents’ investment strategies in such scenarios. In this work, we formulate the optimal investment differential g
This paper investigates the investment problem of constructing an optimal no-short sequential portfolio strategy in a market with a latent dependence structure between asset prices and partly unobservable side information, which is often high-dimensional. The results demonstrate that a dynamic strat
This paper studies the robust reinsurance and investment games for competitive insurers. Model uncertainty is characterized by a class of equivalent probability measures. Each insurer is concerned with relative performance under the worst-case scenario. Insurers’ surplus processes are approximated b
We develop a model based on mean-field games of competitive firms producing similar goods according to a standard AK model with a depreciation rate of capital generating pollution as a byproduct. Our analysis focuses on the widely-used cap-and-trade pollution regulation. Under this regulation, firms
Horizon risk (see arXiv:2301.04971) is studied in the context of cash non-additive fully-dynamic risk measures induced by BSDEs. Furthermore, we introduce a risk measure based on generalized Tsallis entropy which can dynamically evaluate the riskiness of losses considering both horizon risk and inte
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our goal is to understand the impact of the periodic reward struct
We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial distribution with probabilities for a positive return depending