We begin the development of a theory of Banach spaces in the definable setting of o-minimal structures. We outline several results which develop the theory of compact embeddings for explicitly given function spaces. One aim is to explain the substantive underpinnings of an important observation used in the proof of the Reparameterization Theorem of Pila and Wilkie in [2]. We place this observat...

Models of two-player games are analyzed in which contestants strive to maximize relative success (market share). Each contestant divides its resources among a set of investment strategies. For a particular investment strategy the contestants may receive different expected rates of return. Each strategy also returns to both contestants an additional payoff that is unpredictable. Depending on par...

We analyze investment incentives and market structure under oligopoly competition in industries with congestion effects. Our results are particularly focused on models inspired by modern technology-based services, such as telecommunications and computing services. We consider situations where firms compete by simultaneously choosing prices and investments; increasing investment reduces the cong...

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same...

In this paper, we consider the optimal investment problem for an insurer who has n dependent lines of business. The surplus process of the insurer is described by a n-dimensional compound Poisson risk process. Moreover, the insurer is allowed to invest in a risk-free asset and a risky asset whose price process follows the constant elasticity of variance (CEV) model. The investment objective is ...

We analyze investment incentives and market structure under oligopoly competition in industries with congestion effects. Our results are particularly focused on models inspired by modern technology-based services, such as telecommunications and computing services. We consider situations where firms compete by simultaneously choosing prices and investments; increasing investment reduces the cong...

The problem of portfolio optimization is one of the most important issues in asset management. We here propose a new dynamic portfolio strategy based on the time-varying structures of MST networks in Chinese stock markets, where the market condition is further considered when using the optimal portfolios for investment. A portfolio strategy comprises two stages: First, select the portfolios by ...

In tlus paper we consider an investment strategy called dollar-cast-averaging (DCA). It is well known that the argument in favor of DCA is flawed: an investor cannot get something for nothing. Probabilists have made tltis type of flaw precise with theorems like the optional sampling theorem or, more generally, the martingale system theorem (see e.g. [4]). It is interesting that the usual martin...

Understanding the emergence of cooperation in spatial public goods game remains a grand challenge across disciplines. In most previous studies, it is assumed that the investments of all the cooperators are identical, and often equal to 1. However, it is worth mentioning that players are diverse and heterogeneous when choosing actions in the rapidly developing modern society and researchers have...