Superluminal Propagation and Acausality of Nonlinear Massive Gravity

Massive gravity is an old idea: trading geometry for mass. Much effort has been expended on establishing a healthy model, culminating in the current ghost-free version. We summarize here our recent findings -- that it is still untenable -- because it is locally acausal: CTC solutions can be constructed in a small neighborhood of any event.Comment: Contribution to Conference in Honour of the 90th Birthday of Freeman Dyson -- To Appear in Proceeding. v2: Explicit CTC example, and other improvements, adde

Massive gravity acausality redux

Massive gravity (mGR) is a 5(=2s+1)5(=2s+1) degree of freedom, finite range extension of GR. However, amongst other problems, it is plagued by superluminal propagation, first uncovered via a second order shock analysis. First order mGR shock structures have also been studied, but the existence of superluminal propagation in that context was left open. We present here a concordance of these methods, by an explicit (first order) characteristic matrix computation, which confirms mGRʼs superluminal propagation as well as acausality

Problems of Massive Gravities

The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity (mGR) theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed time-like curves (CTCs)/closed causal curves (CCCs)). We extend previous no-go results to the entire three-parameter range of mGR theories. It is also argued that bimetric models suffer a similar fate

Asset allocation decision models in life insurance

The problem of determining the optimal asset allocation strategies for a non-profit life company is approached from a rational decision- making framework. Initially, a number of methods for analysing investment risk are discussed, from which utility theory is felt to be the most appropriate. Stochastic simulation and numerical optimization methods are employed in order to allow more realistic assumptions to be used in these decision models. The multiperiod consumption of dividends is dealt with by considering the expected utility of accumulated dividends, or pay-outs. At first, the case of an open fund is investigated in a static asset allocation framework. In general, the results produced are quite intuitive. At low levels of risk tolerance, the optimal portfolios seem reasonably matched in relation to the liabilities. As the risk tolerance level increases, the preference for matching is seen to reduce. If pay-outs are measured in real terms, greater proportions tend to be invested in the real asset classes. From a mean-variance perspective, the utility maximizing portfolios generally appear to be efficient. However, imposing insolvency constraints on the objective function can have the effect of shifting some of these portfolios away from the efficient frontier. In the case of a closed fund, dynamic asset allocation strategies are investigated. Due to the restrictive assumptions it requires, the possibility of applying dynamic programming in this situation is rejected. Instead, it is proposed that the asset proportions be made functions of the duration of the liabilities, so that the expected utility may be maximized in respect of these function parameters. Overall, this appears to produce reasonable results, although the occasional emergence of less intuitive strategies leaves further scope for refining the treatment of multiperiod consumption