Ruin Theory for Dynamic Spectrum Allocation in LTE-U Networks

LTE in the unlicensed band (LTE-U) is a promising solution to overcome the scarcity of the wireless spectrum. However, to reap the benefits of LTE-U, it is essential to maintain its effective coexistence with WiFi systems. Such a coexistence, hence, constitutes a major challenge for LTE-U deployment. In this paper, the problem of unlicensed spectrum sharing among WiFi and LTE-U system is studied. In particular, a fair time sharing model based on \emph{ruin theory} is proposed to share redundant spectral resources from the unlicensed band with LTE-U without jeopardizing the performance of the WiFi system. Fairness among both WiFi and LTE-U is maintained by applying the concept of the probability of ruin. In particular, the probability of ruin is used to perform efficient duty-cycle allocation in LTE-U, so as to provide fairness to the WiFi system and maintain certain WiFi performance. Simulation results show that the proposed ruin-based algorithm provides better fairness to the WiFi system as compared to equal duty-cycle sharing among WiFi and LTE-U.Comment: Accepted in IEEE Communications Letters (09-Dec 2018

Differentiation of some functionals of risk processes.

For general risk processes, the expected time-integrated negative part of the process on a fixed time interval is introduced and studied. Differentiation theorems are stated and proved. They make it possible to derive the expected value of this risk measure, and to link it with the average total time below zero studied by Dos Reis (1993) and the probability of ruin. Differentiation of other functionals of unidimensional and multidimensional risk processes with respect to the initial reserve level are carried out. Applications to ruin theory, and to the determination of the optimal allocation of the global initial reserve which minimizes one of these risk measures, illustrate the variety of application fields and the benefits deriving from an efficient and effective use of such tools.Ruin theory; Sample path properties; Optimal allocation; Multidimensional risk process; Risk measures

Dynamic pricing of general insurance in a competitive market

A model for general insurance pricing is developed which represents a stochastic generalisation of the discrete model proposed by Taylor (1986). This model determines the insurance premium based both on the breakeven premium and the competing premiums offered by the rest of the insurance market. The optimal premium is determined using stochastic optimal control theory for two objective functions in order to examine how the optimal premium strategy changes with the insurer’s objective. Each of these problems can be formulated in terms of a multi-dimensional Bellman equation. In the first problem the optimal insurance premium is calculated when the insurer maximises its expected terminal wealth. In the second, the premium is found if the insurer maximises the expected total discounted utility of wealth where the utility function is nonlinear in the wealth. The solution to both these problems is built-up from simpler optimisation problems. For the terminal wealth problem with constant loss-ratio the optimal premium strategy can be found analytically. For the total wealth problem the optimal relative premium is found to increase with the insurer’s risk aversion which leads to reduced market exposure and lower overall wealth generation

The management of de-cumulation risks in a defined contribution environment

The aim of the paper is to lay the theoretical foundations for the construction of a flexible tool that can be used by pensioners to find optimal investment and consumption choices in the distribution phase of a defined contribution pension scheme. The investment/consumption plan is adopted until the time of compulsory annuitization, taking into account the possibility of earlier death. The effect of the bequest motive and the desire to buy a higher annuity than the one purchasable at retirement are included in the objective function. The mathematical tools provided by dynamic programming techniques are applied to find closed form solutions: numer-ical examples are also presented. In the model, the trade-off between the different desires of the individual regarding consumption and final annuity can be dealt with by choosing appropriate weights for these factors in the setting of the problem. Conclusions are twofold. Firstly, we find that there is a natural time-varying target for the size of the fund, which acts as a sort of safety level for the needs of the pensioner. Secondly, the personal preferences of the pensioner can be translated into optimal choices, which in turn affect the distribution of the consumption path and of the final annuity