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In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
We consider the optimal investment problem for Black-Scholes type financial market with bounded VaR measure on the whole investment interval $[0,T]$. The explicit form for the optimal strategies is found.
We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the…
We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility.…
We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
This paper considers a utility maximization and optimal asset allocation problem in the presence of a stochastic endowment that cannot be fully hedged through trading in the financial market. After studying continuity properties of the…
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption…
We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and…
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 consider an illiquid financial market with different regimes modeled by a continuous-time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a Cox process with intensity depending on the…
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…
We study a robust utility maximization problem in the case of an incomplete market and logarithmic utility with general stochastic constraints, not necessarily convex. Our problem is equivalent to maximizing of nonlinear expected…
This paper investigates discrete-time Markov decision processes with recursive utilities (or payoffs) defined by the classic CES aggregator and the Kreps-Porteus certainty equivalent operator. According to the classification introduced by…