Related papers: The G-Martingale Approach for G-Utility Maximizati…
We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in continuous time. Both order book depth and resilience are allowed to evolve randomly in time.…
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…
We study a general robust utility maximization problem in a discrete-time frictionless market. The investor is assumed to have a possibly infinite, random, nonconcave, and nondecreasing utility function defined on the whole real line. She…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth. We consider a market model with jumps driven by (multivariate)…
We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has…
We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely…
We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of…
We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…
We investigate optimal consumption problems for a Black-Scholes market under uniform restrictions on Value-at-Risk and Expected Shortfall for logarithmic utility functions. We find the solutions in terms of a dynamic strategy in explicit…
In this paper, we address the stochastic representation problem in discrete time under (non-linear) g-expectation. We establish existence and uniqueness of the solution, as well as a characterization of the solution. As an application, we…
In this article we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein-Zin stochastic differential utility who invests in a constant-parameter Black-Scholes-Merton market. The paper has…
We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the…
This article studies the sensitivity of the power utility maximization problem with respect to the investor's relative risk aversion, the statistical probability measure, the investment constraints and the market price of risk. We extend…
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…
Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for $n$ agents who try to maximize the expected utility of their relative wealth. The utility…