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Exponential functionals of Brownian motion have been extensively studied in financial and insurance mathematics due to their broad applications, for example, in the pricing of Asian options. The Black-Scholes model is appealing because of mathematical tractability, yet empirical evidence shows that geometric Brownian motion does not adequately capture features of market equity returns. One popular alternative for modeling equity returns consists in replacing the geometric Brownian motion by an exponential of a Levy process. In this paper we use this latter model to study variable annuity guaranteed benefits and to compute explicitly the distribution of certain exponential functionals.
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in the correla
We consider a stochastic volatility model with Levy jumps for a log-return process $Z=(Z_{t})_{tgeq 0}$ of the form $Z=U+X$, where $U=(U_{t})_{tgeq 0}$ is a classical stochastic volatility process and $X=(X_{t})_{tgeq 0}$ is an independent Levy proce
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enf
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a n
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitt