Related papers: Existence and Uniqueness for the Multivariate Disc…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
This note contains a short discussion on the sufficiency of finite optimality in martingale transport. It is shown that finitely minimal martingale measures are solutions of the martingale transport problem when the cost function is upper…
For an exponential utility maximizing investment strategy in a Black-Scholes Setting, fixed upper and lower constraints are introduced on the terminal wealth. This is equivalent to combining the optimal strategy with options. The resulting…
We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial…
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in all ``sufficiently volatile'' markets. In our formulation,…
The classical optimal trading problem is the closure of a position in an asset over a time interval; the trader maximizes an expected utility under the constraint that the position be fully closed by terminal time. Since the asset price is…
This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear fractional differential equation with mixed boundary value conditions. Riemann-Liouville fractional derivative is considered. An…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
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 study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
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…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
This paper investigates a continuous-time portfolio optimization problem with the following features: (i) a no-short selling constraint; (ii) a leverage constraint, that is, an upper limit for the sum of portfolio weights; and (iii) a…
This paper investigates a time-inconsistent portfolio selection problem in the incomplete mar ket model, integrating expected utility maximization with risk control. The objective functional balances the expected utility and variance on log…
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,…
We study an optimal liquidation problem with multiplicative price impact in which the trend of the asset's price is an unobservable Bernoulli random variable. The investor aims at selling over an infinite time-horizon a fixed amount of…
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.…