Related papers: Portfolio Optimization under Local-Stochastic Vola…
The standard approach for constructing a Mean-Variance portfolio involves estimating parameters for the model using collected samples. However, since the distribution of future data may not resemble that of the training set, the…
This is a follow up of our previous paper - Trybu{\l}a and Zawisza \cite{TryZaw}, where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…
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,…
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be…
The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and…
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining…
We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional…
We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…
We consider the optimal investment and marginal utility pricing problem of a risk averse agent and quantify their exposure to a small amount of model uncertainty. Specifically, we compute explicitly the first-order sensitivity of their…
We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. In this first paper we explore the need for more general optimization tools, and consider the means by which constrained random…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
We propose an alternative approach towards cost mitigation in volatility-managed portfolios based on smoothing the predictive density of an otherwise standard stochastic volatility model. Specifically, we develop a novel variational Bayes…
We propose a novel portfolio selection approach that manages to ease some of the problems that characterise standard expected utility maximisation. The optimal portfolio is no longer defined as the extremum of a suitably chosen utility…
Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals,…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…