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In an incomplete financial market with general continuous semimartingale dynamics; we model an investor with log-utility preferences who, in addition to an initial capital, receives units of a non-traded endowment process. Using duality…
The aim of this paper is to investigate the impact of rebalancing frequency and transaction costs on the log-optimal portfolio, which is a portfolio that maximizes the expected logarithmic growth rate of an investor's wealth. We prove that…
We consider a discrete-time model of a financial market where a risky asset is bought and sold with transactions having a transient price impact. It is shown that the corresponding utility maximization problem admits a solution. We manage…
In the paper, a mean-square minimization problem under terminal wealth constraint with partial observations is studied. The problem is naturally connected to the mean-variance hedging problem under incomplete information. A new approach to…
This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be…
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…
This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In…
In this paper, we obtain a duality result for the exponential utility maximization problem where trading is subject to quadratic transaction costs and the investor is required to liquidate her position at the maturity date. As an…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is…
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish…
The scope of this paper is to study the optimal stopping problems associated to a stochastic process, which may represent the gain of an investment, for which information on the final value is available a priori. This information may…
In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process,…
We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool. At the…
The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the…
We propose a mathematical model for one pattern of charts studied in technical analysis: in a phase of consolidation, the price of a risky asset goes down $\xi$ times after hitting a resistance level. We construct a mathematical strategy…
We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular,…
Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the…
In this work we study a continuous time exponential utility maximization problem in the presence of a linear temporary price impact. More precisely, for the case where the risky asset is given by the Ornstein-Uhlenbeck diffusion process we…
In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin…