“Semi-stochastic” or “piecewise-deterministic” Markov processes generalize continuous-time Markov chains, allowing for deterministic flow between Markovian jumps. They have been employed as models for the effect of environmental catastrophes on biological populations, for the progress of...

Over the last two decades, default rates and market risk have increased substantially. A consequence of the growing global interlacing is a strong dependence between both individual stock returns and credit events. Risk management (especially risk diversification) is much more challenging,...

In this study, we investigate two multivariate time-changed Brownian motion option pricing models in which the connection between the historical measure P and the risk-neutral measure Q is given by the Esscher transform. The models incorporate skewness, kurtosis and more complex dependence...

We present a comprehensive framework for comparing the merits of alternative portfolio insurance strategies in realistic contexts. Our findings add generality to previous results comparing option based and constant proportionality portfolio insurance strategies (OBPI and CPPI). The optimal OBPI...

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the...

In this paper we consider a generalization of one of the earliest models of an asset price, namely the Black–Scholes model, which captures the subdiffusive nature of an asset price dynamics. We introduce the geometric Brownian motion time-changed by infinitely divisible inverse subordinators,...

The main purpose of this article is to propose computational methods for Greeks and the multidimensional density estimation for an asset price dynamics model defined with time-changed Brownian motions. Our approach is based on an application of the Malliavin integration-by-parts formula on the...

Constant proportion portfolio insurance (CPPI) strategies implemented in continuous time on asset prices following geometric Brownian processes are expected utility maximising for investors with HARA utilities. But, in reality, these strategies are implemented in discrete time and asset prices...