Related papers: Large losses - probability minimizing approach
Solving large-scale robust portfolio optimization problems is challenging due to the high computational demands associated with an increasing number of assets, the amount of data considered, and market uncertainty. To address this issue, we…
We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal…
In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate…
Individual investors are now massively using online brokers to trade stocks with convenient interfaces and low fees, albeit losing the advice and personalization traditionally provided by full-service brokers. We frame the problem faced by…
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by…
We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
Entropy based ideas find wide-ranging applications in finance for calibrating models of portfolio risk as well as options pricing. The abstracted problem, extensively studied in the literature, corresponds to finding a probability measure…
In financial investing, universal portfolios are a means of constructing portfolios which guarantee a certain level of performance relative to a baseline, while making no statistical assumptions about the future market data. They fall under…
We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small…
The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with…
It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks.…
The problem of quantile hedging for basket derivatives in the Black-Scholes model with correlation is considered. Explicit formulas for the probability maximizing function and the cost reduction function are derived. Applicability of the…
We introduce a neural network approach for assessing the risk of a portfolio of assets and liabilities over a given time period. This requires a conditional valuation of the portfolio given the state of the world at a later time, a problem…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting…
We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo…
Portfolio optimization approaches inevitably rely on multivariate modeling of markets and the economy. In this paper, we address three sources of error related to the modeling of these complex systems: 1. oversimplifying hypothesis; 2.…
Financial markets have developed a lot of strategies to control risks induced by market fluctuations. Mathematics has emerged as the leading discipline to address fundamental questions in finance as asset pricing model and hedging…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…