相关论文: Measuring and hedging financial risks in dynamical…

The aim of these lectures at MITACS-PIMS-UBC Summer School in Risk Man- agement and Risk Sharing is to discuss risk controlled approaches for the pricing and hedging of financial risks. We will start with the classical dual approach for…

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…

In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…

Machine learning models are increasingly used in a wide variety of financial settings. The difficulty of understanding the inner workings of these systems, combined with their wide applicability, has the potential to lead to significant new…

As soon as one accepts to abandon the zero-risk paradigm of Black-Scholes, very interesting issues concerning risk control arise because different definitions of the risk become unequivalent. Optimal hedges then depend on the quantity one…

Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…

In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected…

Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events,…

Delta hedging, which plays a crucial r\^ole in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of…

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…

Proof that under simple assumptions, such as constraints of Put-Call Parity, the probability measure for the valuation of a European option has the mean derived from the forward price which can, but does not have to be the risk-neutral one,…

In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…

Recurring international financial crises have adverse socioeconomic effects and demand novel regulatory instruments or strategies for risk management and market stabilization. However, the complex web of market interactions often impedes…

We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms…

The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…

One of the crucial problems in mathematical finance is to mitigate the risk of a financial position by setting up hedging positions of eligible financial securities. This leads to focusing on set-valued maps associating to any financial…

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or…

Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…

This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical…

We provide a new dynamic approach to scenario generation for the purposes of risk management in the banking industry. We connect ideas from conventional techniques -- like historical and Monte Carlo simulation -- and we come up with a…