Related papers: Outperforming the market portfolio with a given pr…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the…
We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…
The strong relative arbitrage problem in Stochastic Portfolio Theory seeks an investment strategy that almost surely outperforms a benchmark portfolio at the end of a given time horizon. The highest relative return in relative arbitrage…
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 are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market…
We study pricing and (super)hedging for American options in an imperfect market model with default, where the imperfections are taken into account via the nonlinearity of the wealth dynamics. The payoff is given by an RCLL adapted process…
In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…
In a two-period financial market where a stock is traded dynamically and European options at maturity are traded statically, we study the so-called martingale Schr\"odinger bridge Q*; that is, the minimal-entropy martingale measure among…
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…
In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent…
We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form…
In a semimartingale financial market model, it is shown that there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale…
In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the…
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 establish the existence and characterization of a primal and a dual facelift - discontinuity of the value function at the terminal time - for utility-maximization in incomplete semimartingale-driven financial markets. Unlike in the…
We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to $n$-marginal Skorokhod embedding problem in Ob{\l}\'oj and…
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal…