Stochastic Control & Optimal Stopping

Introduced in the late 90s, the passport option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem that for $d>1$ risky assets remains an open problem. Even in a

We propose a virtual bidding strategy by modeling the price differences between the day-ahead market and the real-time market as Brownian motion with drift, where the drift rate and volatility are functions of meteorological variables. We then transform the virtual bidding problem into a mean-varian

We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems in terms of a system of backward stochastic differential eq

We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. This resilience is modeled through a potentially arbitrary limit-order book shape. T

We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon-Loeb model, each attack may re

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker’s control is represented by the probability of stopping within a given time-

This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state spaces and the intricacies of selecting appropriate risk penalty

This article explores the optimisation of trading strategies in Constant Function Market Makers (CFMMs) and centralised exchanges. We develop a model that accounts for the interaction between these two markets, estimating the conditional dependence between variables using the concept of conditional

We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the presence of transaction costs under discrete trading schedules. We

This paper investigates optimal investment and pension policies in a Pay-As-You-Go (PAYG) system supplemented by a buffer fund used as an intergenerational risk-sharing mechanism. The social planner’s preference criterion is represented by non-zero volatility forward Constant Relative Risk Aversion

Banks must optimize risky investments, dividend payouts, and capital structure under tight Basel III solvency and liquidity constraints, while costly equity issuance serves as a distress-recovery tool. We formulate this as a stochastic control problem that reduces the high-dimensional balance-sheet

The growing prevalence of drift and shocks in modern decision environments exposes a gap between classical optimization theory and real-world practice. Standard models assume fixed objectives, yet organizations from hospitals to power grids routinely adapt to shifting priorities, noisy data, and abr

This Ph.D. thesis explores approximations and regularity for the Heston stochastic volatility model through three interconnected works. The first work focuses on developing high-order weak approximations for the Cox-Ingersoll-Ross (CIR) process, essential for financial modelling but challenging due

We find the equilibrium contract that an automated market maker (AMM) offers to their strategic liquidity providers (LPs) in order to maximize the order flow that gets processed by the venue. Our model is formulated as a leader-follower stochastic game, where the venue is the leader and a representa

We characterise the solutions to a continuous-time optimal liquidity provision problem in a market populated by informed and uninformed traders. In our model, the asset price exhibits fads – these are short-term deviations from the fundamental value of the asset. Conditional on the value of the fad,

In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling constraints and borrowing prohibition. The optimal feedback

We address the liquidation problem arising from the credit risk management in decentralised finance (DeFi) by formulating it as an ergodic optimal control problem. In decentralised derivatives exchanges, liquidation is triggered whenever the parties fail to maintain sufficient collateral for their o

We investigate the optimal investment-reinsurance problem for insurance company with partial information on the market price of the risk. Through the use of filtering techniques we convert the original optimization problem involving different filtrations, into an equivalent stochastic control proble

We consider an insurance company which faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g. at the end of an accounting period) and the ruin probability in a finite time interval by purcha

This paper studies the equity holders’ mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the multi-dimensional Black-Scholes model, showing the existence o