Related papers: An explicit formula for optimal portfolios in comp…
We use pathwise It\^o calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of F\"ollmer's pathwise It\^o calculus and works for…
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…
The portfolio optimization problem is a basic problem of financial analysis. In the study, an optimization model for constructing an options portfolio with a certain payoff function has been proposed. The model is formulated as an integer…
We provide a simple and straightforward approach to a continuous-time version of Cover's universal portfolio strategies within the model-free context of F\"ollmer's pathwise It\^o calculus. We establish the existence of the universal…
Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that by using…
Insider information and model uncertainty are two unavoidable problems for the portfolio selection theory in reality. This paper studies the robust optimal portfolio strategy for an investor who owns general insider information under model…
Functional It^o calculus is based on an extension of the classical It^o calculus to functionals depending on the entire past evolution of the underlying paths and not only on its current value. The calculus builds on Follmer's…
This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of…
Financial portfolio optimization is a widely studied problem in mathematics, statistics, financial and computational literature. It adheres to determining an optimal combination of weights associated with financial assets held in a…
We consider optimal investment problems for a diffusion market model with non-observable random drifts that evolve as an Ito's process. Admissible strategies do not use direct observations of the market parameters, but rather use historical…
We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in…
We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected…
We study an optimal portfolio problem designed for an agent operating in intraday electricity markets. The investor is allowed to trade in a single risky asset modelling the continuously traded power and aims to maximize the expected…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that…
We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Ito integrals of which components all belong to the same fixed Wiener chaos. Combining Malliavin calculus, Stein's method…
We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of…
We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing…
We aim to construct a general framework for portfolio management in continuous time, encompassing both stocks and bonds. In these lecture notes we give an overview of the state of the art of optimal bond portfolios and we re-visit main…