On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile.
Front matter
The Equadiff is a series of biannual conferences on mathematical analysis, numerical approximation and applications of differential equations. Proceedings of Equadiff 2017 Conference contain peer-reviewed contributions of participants of the conference. The proceedings cover a wide range of topics presented by plenary, minisymposia and contributed talks speakers. The scope of papers ranges from ordinary differential equations, differential inclusions and dynamical systems towards qualitative and...
The C stability of slow manifolds for a system of singularly perturbed evolution equations
In this paper we investigate the singular limiting behavior of slow invariant manifolds for a system of singularly perturbed evolution equations in Banach spaces. The aim is to prove the C stability of invariant manifolds with respect to small values of the singular parameter.
Limiting behavior of global attractors for singularly perturbed beam equations with strong damping
The limiting behavior of global attractors for singularly perturbed beam equations is investigated. It is shown that for any neighborhood of the set is included in for small.
Existence and limiting behaviour for damped nonlinear evolution equations with nonlocal terms
On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...
Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation () based Sharpe ratio for measuring...
Computational studies of conserved mean-curvature flow
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is solved numerically and several computational studies are...
Dynamic Stochastic Accumulation Model With Application to Pension Savings Management
Page 1