Growth-security profiles in capital accumulation under risk (Q1176863)

This paper discusses the relation between growth and security dimensions in investment decisions under risk. A process of capital accumulation is, in general, subject to rates of return that vary stochastically. An investment strategy is described by proportions, at each point in time, of the capital invested in \(n\) risky and one risk-free instruments. Both the long term expectation of capital growth and the probability of realizing given minimum growth are functionally related to the strategy and define a profile of capital accumulation. The efficient frontier comprises maximum growth values for given levels of security. Selecting a particular profile and assuming a simple return function allows to define optimal growth and security strategies which then can be shown to be deterministic or time-separable, i.e. independent of the history of capital accumulation. Either strategy leads to a point on the efficient frontier. The second main result establishes that growth can be continuously traded for security along the path given by convex combinations of the two optimal strategies. The path does not coincide with the efficient frontier although the authors assume it to be close to the latter. They can finally show that a lower boundary for this path exists.