All posts under category "Quantitative Finance / Q-Fin.PM"
We propose a mathematical framework for the study of a family of random fields--called forward performances--which arise as numerical representation of certain rational preference relations in mathematical finance. Their spatial structure corresponds to that of utility functions, while the temporal
We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and
We examine three methods of constructing correlated Student-$t$ random variables. Our motivation arises from simulations that utilise heavy-tailed distributions for the purposes of stress testing and economic capital calculations for financial institutions. We make several observations regarding the
We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cram'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value func
Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and
Flexible algorithm of multicurrency trade on Forex market has been built on the grounds of non-linear stochastic wavelets (NSW) model. Probability of the loss-free trade has been evaluated. Results of the algorithm's real-time testing and issues of the algorithm's development are discussed.
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 rational decisions that would absolutely minimize the risk. He
This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and {O}ksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the con
In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function f
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