POTENTIAL GAMES WITH AGGREGATION IN NON-COOPERATIVE GENERAL INSURANCE MARKETS

AbstractIn the global insurance market, the number of product-specific policies from different companies has increased significantly, and strong market competition has boosted the demand for a competitive premium. Thus, in the present paper, by considering the competition between each pair of insurers, an N-player game is formulated to investigate the optimal pricing strategy by calculating the Nash equilibrium in an insurance market. Under that framework, each insurer is assumed to maximise its utility of wealth over the unit time interval. With the purpose of solving a game of N-players, the best-response potential game with non-linear aggregation is implemented. The existence of a Nash equilibrium is proved by finding a potential function of all insurers' payoff functions. A 12-player insurance game illustrates the theoretical findings under the framework in which the best-response selection premium strategies always provide the global maximum value of the corresponding payoff function.</jats:p

A high order finite element scheme for pricing options under regime switching jump diffusion processes

This paper considers the numerical pricing of European, American and Butterfly options whose asset price dynamics follow the regime switching jump diffusion process. In an incomplete market structure and using the no-arbitrage pricing principle, the option pricing problem under the jump modulated regime switching process is formulated as a set of coupled partial integro-differential equations describing different states of a Markov chain. We develop efficient numerical algorithms to approximate the spatial terms of the option pricing equations using linear and quadratic basis polynomial approximations and solve the resulting initial value problem using exponential time integration. Various numerical examples are given to demonstrate the superiority of our computational scheme with higher level of accuracy and faster convergence compared to existing methods for pricing options under the regime switching model

The Benefits of Schooling: A Human Capital Alocation into a Continuous Optimal Control Framework

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Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach

A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based frequency response function (FRF) is determined for a linear structural system with singular matrices. Next, relying on the M-P FRF a spectral input-output (excitation-response) relationship is derived in the frequency domain for determining the linear system response power spectrum. Further, the above methodology is extended via statistical linearization to account for nonlinear systems. This leads to an iterative determination of the system response mean vector and covariance matrix. Furthermore, to account for singular matrices, the generalization of a widely utilized formula that facilitates the application of statistical linearization is proved as well. The formula relates to the expectation of the derivatives of the system nonlinear function and is based on a Gaussian response assumption. Several linear and nonlinear MDOF structural systems with singular matrices are considered as numerical examples for demonstrating the validity and applicability of the developed frequency domain methodology