Optimal Control of Investment-Reinsurance Problem for an Insurer with Jump-Diffusion Risk Process: Independence of Brownian Motions

This paper investigates the excess-of-loss reinsurance and investment problem for a compound Poisson jump-diffusion risk process, with the risk asset price modeled by a constant elasticity of variance (CEV) model. It aims at obtaining the explicit optimal control strategy and the optimal value function. Applying stochastic control technique of jump diffusion, a Hamilton-Jacobi-Bellman (HJB) equation is established. Moreover, we show that a closed-form solution for the HJB equation can be found by maximizing the insurer’s exponential utility of terminal wealth with the independence of two Brownian motions W(t) and W1(t). A verification theorem is also proved to verify that the solution of HJB equation is indeed a solution of this optimal control problem. Then, we quantitatively analyze the effect of different parameter impacts on optimal control strategy and the optimal value function, which show that optimal control strategy is decreasing with the initial wealth x and decreasing with the volatility rate of risk asset price. However, the optimal value function V(t;x;s) is increasing with the appreciation rate μ of risk asset

An optimal investment strategy with maximal risk aversion and its ruin probability

Abstract Let W = (W(i))(i is an element of N) he an infinite dimensional Brownian motion and (X(t))(1 >= 0) a continuous adapted n-dimensional process. Set tau(R) = infit : X(t) - x(t)vertical bar, where x(t-t) >= 0 is a R(n)-valued deterministic differentiable curve and R(t) > 0, t > 0 a time-dependent radius. We assume that, up to tau(R), the process X solves the following (not necessarily Markov) SDE : X(t Lambda tau R) = x + Sigma(infinity)(j=1) integral(t Lambda tau R)(0) sigma(j) (s, omega, X(s))dW(s)(j) + integral(t Lambda tau R)(0) b(s, omega, X(s))ds. Under local conditions on the coefficients, we obtain lower bounds for P (tau(R) >= T) as well as estimates for distribution functions and expectations. These results are discussed in the elliptic and log-normal frameworks. An example of a diffusion process that satisfies the weak Hormander condition is also given. (C) 2011 Elsevier B.V. All rights reserved

An Analysis of Investments by Multilateral Development Banks in Central America

Multilateral development banks (MDBs) are under increased pressure to justify their allocation of donor resources. These funds help produce growth in developing regions such as Central America (CA), where wealth inequality limits individuals\u27 access to basic services and increases the prevalence of crime and corruption. MDB leaders are not always confident the allocation of limited resources creates optimal value. The capital asset price model (CAPM) was the theoretical framework of this correlational study. Archival data consisting of annual reports and audited financial statements were used to draw a sample (N = 66) of USD $4.857-asset valued loans made by MDBs between 1995-2013 in 7 CA countries. Regression analysis was used to determine the significance of relationships between the independent variables including the risk-free rate of return (Rf), volatility of a project (βp), and expected return on the market (Rm) and the dependent variable, the expected return (rp) used by MDBs. No evidence of a statistically significant relationship between the expected return of individual loans (adjusted for risk-free rate, volatility, and market return) and the expected return used by MDBs was found using correlational analysis. Findings from multiple regression analysis indicated that the expected return used by MDBs underperforms risk-adjusted market expectations. Study findings may help MDB leaders to promote business development and social welfare in CA through private investments, which may result in positive social change