Decisions in Economics and Finance最新文献

We consider the reinsurance-investment problem under the mean variance criterion in a dynamic contagion model that takes into account self and externally excited claim clustering effects. We find explicit time-consistent reinsurance-investment strategies for a generalized proportional contract in which only losses above a certain level are reinsured. This greater flexibility in the contract mitigates the possible drawback of the primary insurer ceding too much at the expense of profitability, while still ensuring that the higher risks are shared with the reinsurance counterparty.

Special-rate life annuities offer customized annuity rates, based on the lifestyle or health status of the individual. Their main purpose is to encourage the annuity demand, which is still underdeveloped in many markets; as better annuity rates are quoted for individuals showing a higher mortality profile, the number of individuals attracted by life annuities could increase. Providers should then gain larger pool sizes; however, this is possibly matched by a greater heterogeneity of the pool, due to several risk classes defined by the annuity design. Heterogeneity emerges not only in terms of different life expectancies, but also in respect of the dispersion of the lifetime distribution; indeed, situations resulting in a lower life expectancy also show greater variability of the lifetime. As it is well-known, pooling effects are reinforced by the pool size, while they are weakened by its heterogeneity, with a possibly unclear impact on the overall longevity risk to which the provider is exposed. In this paper we investigate the longevity risk profile of an annuity pool consisting of several risk classes. We consider both the idiosyncratic and aggregate components of the risk, by modelling the random number of deaths and assuming a stochastic mortality dynamics. The heterogeneity of risk classes is represented alternatively in a deterministic and stochastic setting. Our conclusions are in line with similar findings discussed in the literature, but obtained in a deterministic framework. Results suggest that the longevity risk profile of the provider is not significantly undermined by a greater pool heterogeneity, with a prevalence of the aggregate component whatever the pool composition.

We study a single period newsvendor problem under ambiguity in the presence of a discrete random demand. Ambiguity is introduced in the model by (epsilon )-contaminating the newsvendor’s prior probability measure with respect to two suitable classes of probability measures, assuring that the lower expected demand and the upper expected demand are both equal to the prior expected demand. Assuming that the newsvendor has a pessimistic attitude towards ambiguity, we characterize the order quantity that either maximizes the lower expected profit or minimizes the upper expected loss. Since the two contamination classes are cores of two distinct belief functions, we show that the maximin and minimax problems translate in the maximization and minimization of two distinct Choquet integrals.

In a probabilistic mean-field game driven by a linear diffusion an individual player aims to minimize an ergodic long-run cost by controlling the diffusion through a pair of –increasing and decreasing– càdlàg processes, while he is interacting with an aggregate of players through the expectation of a similar diffusion controlled by another pair of càdlàg processes. In order to find equilibrium points in this game, we first consider the control problem, in which the individual player has no interaction with the aggregate of players. In this case, we prove that the best policy is to reflect the diffusion process within two thresholds. Based on these results, we obtain criteria for the existence of equilibrium points in the mean-field game in the case when the controls of the aggregate of players are of reflection type, and give a pair of nonlinear equations to find these equilibrium points. In addition, we present an approximation result for nash equilibria of erdogic games with finitely many players to the mean-field game equilibria considered above when the number of players tends to infinity. These results are illustrated by several examples where the existence and uniqueness of the equilibrium points depend on the coefficients of the underlying diffusion.

This paper studies the linkages between different aspects of preferences in the presence of risk increases of different degrees in the variance of consumption. We find that the effects on expected utility of risk increases in variance of consecutive degrees are in opposite directions. Applying this result to saving choice when either labour income or the interest rate is random, we obtain that the effects on the optimal level of saving of risk increases in variance of subsequent degrees are in opposite directions. Lastly, similar results are obtained for risk increases in the variance of the variance of consumption.

This piece in the Milestones series is dedicated to the paper “Specimen Theoriae Novae de Mensura Sortis ” by Daniel Bernoulli, published in 1738 on the Commentarii Academiae Scientiarum Imperialis Petropolitanae.

In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error of the hedging strategy at maturity. Specifically, the algorithm moves backward in time, determining, for each time-step and different market states, the optimal hedging strategy that minimizes the loss function at the time the option is exercised, by assuming that the strategy used in the future for hedging the liability is the one determined at the previous steps of the algorithm. The proposed approach only employs classic techniques, such as an optimization algorithm, Monte Carlo simulation, and interpolation on a grid. Above all, our choice of a backward iterating approach addresses the issue of time-inconsistency inherent in many traditional risk measures, compelling the optimal strategy to maintain consistency over time, even though the original problem might not inherently support such consistency. Comparisons with the Deep Hedging algorithm in various numerical experiments showcase the efficiency and accuracy of the proposed method.

We propose in this paper a method for verifying the non-existence of anatocism in a periodic amortization with n periodic installments, by the replication of its cash flows. The cash flows are obtained by recursively constructing an appropriate sequence of n consecutive single period loans, at the periodic interest rate i, each one with repayment of principal and interest at the end of the single period. Since each elementary transaction is concluded within one time unit, there is no possibility of interest accruing on interest and hence anatocism is ruled out. Therefore, this characteristic must be acknowledged to be valid also for the loan amortization schedule with n periodic installments whose cash flows are perfectly replicated by the unique loan sequence obtained.

Risk measures satisfying the axiom of comonotonic additivity are extensively studied, arguably because of the plethora of results indicating interesting aspects of such risk measures. Recent research, however, has shown that this axiom is incompatible with properties that are central in specific contexts. In this paper, we present a literature review of these incompatibilities. Specifically, we highlight the conflict between comonotonic additivity and surplus invariance, eligible assets, elicitabilty, and dynamic consistency.