Related papers: State-dependent utility maximization in L\'evy mar…
We consider a multi-stock continuous time incomplete market model with random coefficients. We study the investment problem in the class of strategies which do not use direct observations of the appreciation rates of the stocks, but rather…
We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by…
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.…
In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential…
We revisit the classical Merton consumption--investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $\alpha$-integral, interpolating between It\^{o}, Stratonovich, and…
We treat utility maximization from terminal wealth for an agent with utility function $U:\mathbb{R}\to\mathbb{R}$ who dynamically invests in a continuous-time financial market and receives a possibly unbounded random endowment. We prove the…
We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be…
This paper studies Merton's problem in an extended formulation by incorporating the benchmark tracking on the wealth process. We consider a tracking formulation where the fund manager aims to maximize the trade-off between the expected…
In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the num\'eraire-based model and work with utility…
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem,…
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the…
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…
In an incomplete model, where under an appropriate num\'eraire, the stock price process is driven by a sigma-bounded semimartingale, we investigate the behavior of the expected utility maximization problem under small perturbations of the…
We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an $R^d$-valued continuous…
The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial…
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…
This paper is mainly a survey of recent research developments regarding methods for risk minimization in financial markets modeled by It\^o-L\'evy processes, but it also contains some new results on the underlying stochastic maximum…
This article is devoted to the maximisation of HARA utilities of L{\'e}vy switching process on finite time interval via dual method. We give the description of all f-divergence minimal martingale measures in initially enlarged filtration,…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain…