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We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists…
We consider a structural stochastic volatility model for the loss from a large portfolio of credit risky assets. Both the asset value and the volatility processes are correlated through systemic Brownian motions, with default determined by…
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space…
We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets' growth rate processes…
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
The stock market offers a platform where people buy and sell shares of publicly listed companies. Generally, stock prices are quite volatile; hence predicting them is a daunting task. There is still much research going to develop more…
The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…
This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve…
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 paper studies a non-stochastic version of Fernholz's stochastic portfolio theory for a simple model of stock markets with continuous price paths. It establishes non-stochastic versions of the most basic results of stochastic portfolio…
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. We first propose a general problem formulation aimed at finding a portfolio of underlying component assets by…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
Robust estimation for modern portfolio selection on a large set of assets becomes more important due to large deviation of empirical inference on big data. We propose a distributionally robust methodology for high-dimensional mean-variance…
The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…
Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new…
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…
This manuscript reports a stochastic dynamical scenario whose associated stationary probability density function is exactly a previously proposed one to adjust high-frequency traded volume distributions. This dynamical conjecture,…
In stochastic finance, one traditionally considers the return as a competitive measure of an asset, {\it i.e.}, the profit generated by that asset after some fixed time span $\Delta t$, say one week or one year. This measures how well (or…
The aim of this work consists in the study of the optimal investment strategy for a behavioural investor, whose preference towards risk is described by both a probability distortion and an S-shaped utility function. Within a continuous-time…