In this paper, we analyse a market where the risky assets follow exponential additive processes, which can be viewed as time‐inhomogeneous generalizations of geometric Levy processes. In this market we show that, when an investor wants to maximize a CRRA utility function of his/her terminal wealth, his/her optimal strategy consists in keeping proportions of wealth in the risky assets which depend only on time but not on the current wealth level or on the prices of the risky assets. In the time‐homogeneous case, the optimal strategy is to keep constant proportions of wealth, a result already found by Kallsen which extends the classical Merton’s result to this market. While the one‐dimensional case has been extensively treated and the multidimensional case has been treated only in the time‐homogeneous case Callegaro and Vargiolu (2009), Kallsen (2000), and Korn et al. (2003) to the authors’ knowledge this is the first time that such results are obtained for exponential additive processes in the multidimensional case. We use these results to show that the optimal solution in the presence of jumps has the form of the analogous one without jumps but with the asset yields vector reduced by suitable quantities: in the one‐dimensional case, we extend a result by Benth et al. (2001). We conclude with four examples.

We analyze a class of 'large group' Chamberlinian monopolistic competition models using multiplicatively quasi-separable (MQS) and additively quasi-separable (AQS) functions. We first prove that the MQS and AQS functions are equivalent to the 'constant relative risk aversion' (CRRA) and 'constant absolute risk aversion' (CARA) classes of functions, respectively. Whereas both approaches allow for closed-form solutions, only the AQS functions yield profit-maximizing prices that decrease in the mass of competing firms. We then characterize the equilibrium in both cases and discuss some possible applications of the AQS framework to trade, growth, and development.

This paper investigates a stochastic differential portfolio game between two competing investors with relative wealth preferences. The financial market consists of one risk-free asset and one risky asset, whose price dynamics follow the CEV model. We formulate this game as two utility maximization problems, where each investor aims to maximize their relative utility defined as the weighted average of the ratio between their terminal wealth and the competitor’s terminal wealth. Firstly, we derive the Hamilton–Jacobi–Bellman (HJB) equations and corresponding value functions through the dynamic programming principle. Next, we obtain the explicit solutions to equilibrium investment strategies and value functions for the non-zero-sum game under the CRRA utility framework. Finally, we conducted numerical simulations to analyze the impacts of model parameters on equilibrium strategies and provide relevant economic explanations.

We give the explicit form of the survival process of the default time [Formula: see text] modeled by the generalized Cox process model. Then we derive the dynamic CRRA-utility indifference value (UIV) Ct of the 𝔽-investors with respect to the 𝔾-investors and describe the dynamics of Ct by two BSDEs. Finally, we give an example in which we can give the explicit expression of Ct. For the generalized Cox process model we typically have that Ct ≥ 1 in contrast to the standard Cox process model.