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In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional It\^o calculus approach, we overcome the non-Markovian and…
The Black-Scholes-Merton model is a mathematical model for the dynamics of a financial market that includes derivative investment instruments, and its formula provides a theoretical price estimate of European-style options. The model's…
We study and solve the worst-case optimal portfolio problem as pioneered by Korn and Wilmott (2002) of an investor with logarithmic preferences facing the possibility of a market crash with stochastic market coefficients by enhancing the…
We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply the duality methods developed in previous work to…
We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
The classical Merton investment problem predicts deterministic, state-dependent portfolio rules; however, laboratory and field evidence suggests that individuals often prefer randomized decisions leading to stochastic and noisy choices.…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic…
We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$.…
In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for…
We price European and American exchange options where the underlying asset prices are modelled using a Merton (1976) jump-diffusion with a common Heston (1993) stochastic volatility process. Pricing is performed under an equivalent…
This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic…
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation.…
In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional…
In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…
An optimal control problem is considered for a stochastic differential equation with the cost functional determined by a backward stochastic Volterra integral equation (BSVIE, for short). This kind of cost functional can cover the general…
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
We consider a mean-field control problem with c\`adl\`ag semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state…
This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without…