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.
In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an explicit solution for the Merton portfolio problem when an as
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in order to keep the time-space process $(t,X_t)$ inside the set $\
A theoretical model of systemic-risk propagation of financial market is analyzed for stability. The state equation is an unsteady diffusion equation with a nonlinear logistic growth term, where the diffusion process captures the spread of default stress between interconnected financial entities and
We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [“BS24”]. These examples and counterexamples do not only illustrate the results obtained in [“BS24”], but show the limitations of the results and the sharpness of the
In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case where the risky asset is given by a Gaussian process (with so
In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from non-exponential discount functions. We characterize the sol
This paper analyzes the 1/3 Financial Rule, a method of allocating income equally among debt repayment, savings, and living expenses. Through mathematical modeling, game theory, behavioral finance, and technological analysis, we examine the rule’s potential for supporting household financial stabili
The Nobel-price winning Mirrlees’ theory of optimal taxation inspired a long sequence of research on its refinement and enhancement. However, an issue of concern has been always the fact that, as was shown in many publications, the optimal schedule in Mirrlees’ paradigm of maximising the total utili
This paper diverges from previous literature by considering the utility maximization problem in the context of investors having the freedom to actively acquire additional information to mitigate estimation risk. We derive closed-form value functions using CARA and CRRA utility functions and establis
Standard real options theory predicts delay in exercising the option to invest or deploy when extreme asset volatility or technological uncertainty are present. However, in the current race to develop artificial general intelligence (AGI), sovereign actors are exhibiting behaviors contrary to theore
We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.
We develop a fitted value iteration (FVI) method to compute bicausal optimal transport (OT) where couplings have an adapted structure. Based on the dynamic programming formulation, FVI adopts a function class to approximate the value functions in bicausal OT. Under the concentrability condition and