Related papers: On regularized optimal execution problems and thei…
This paper studies the problem of optimally extracting nonrenewable natural resource in light of various financial and economic restrictions and constraints. Taking into account the fact that the market values of the main natural resources…
We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and…
This paper revisits the classical Merton portfolio choice problem over infinite horizon for high risk aversion, addressing technical challenges related to establishing the existence and identification of optimal strategies. Traditional…
We investigate an optimal investment problem with a general performance criterion which, in particular, includes discontinuous functions. Prices are modeled as diffusions and the market is incomplete. We find an explicit solution for the…
In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We…
This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the…
We solve an expected utility-maximization problem with a Value-at-risk constraint on the terminal portfolio value in an incomplete financial market due to stochastic volatility. To derive the optimal investment strategy, we use the dynamic…
We study a continuous-time portfolio choice problem for an investor whose state-dependent preferences are determined by an exogenous factor that evolves as an It\^o diffusion process. Since risk attitudes at the end of the investment…
Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are…
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas…
We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures…
This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with…
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…
We deal with the optimal execution problem when the broker's goal is to reach a performance barrier avoiding a downside barrier. The performance is provided by the wealth accumulated by trading in the market, the shares detained by the…
We consider the valuation problem of an (insurance) company under partial information. Therefore we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…