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We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the…
Providing a measure of market risk is an important issue for investors and financial institutions. However, the existing models for this purpose are per definition symmetric. The current paper introduces an asymmetric capital asset pricing…
In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…
We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that 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.…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
We consider a market consisting of one safe and one risky asset, which offer constant investment opportunities. Taking into account both proportional transaction costs and linear price impact, we derive optimal rebalancing policies for…
This paper focuses on the developing of high-dimensional risk models to construct portfolios of securities in the US stock exchange. Investors seek to gain the highest profits and lowest risk in capital markets. We have developed various…
This study provides a practical introduction to high-frequency trading in blockchain-based currency markets. These types of markets have some specific characteristics that differentiate them from the stock markets, such as a large number of…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…
Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
In Electricity markets, illiquidity, transaction costs and market price characteristics prevent managers to replicate exactly contracts. A residual risk is always present and the hedging strategy depends on a risk criterion chosen. We…
This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized…
We propose a portfolio approach for operational risk quantification based on a class of analytical models from which we derive new results on the correlation problem. In particular, we show that uniform correlation is a robust assumption…
We survey systemic risks to financial markets and present a high-level description of an algorithm that measures systemic risk in terms of coupled networks.
We consider a multivariate financial market with transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in…
Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The…