Related papers: Several expressions of the net single premiums und…
We consider the problem of how an individual can use term life insurance to maximize the probability of reaching a given bequest goal, an important problem in financial planning. We assume that the individual buys instantaneous term life…
In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time…
We determine the optimal amount of life insurance for a household of two wage earners. We consider the simple case of exponential utility, thereby removing wealth as a factor in buying life insurance, while retaining the relationship among…
We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $ \mu $, diffusing in one dimension. The particle starts its motion from $ x>0 $ and it is subject to stochastic resetting with constant rate $…
This paper considers the pricing of equity-linked life insurance contracts with death and survival benefits in a general model with multiple stochastic risk factors: interest rate, equity, volatility, unsystematic and systematic mortality.…
Dependence among multiple lifetimes is a key factor for pricing and evaluating the risk of joint life insurance products. The dependence structure can be exposed to model uncertainty when available data and information are limited. We…
A possibly immortal agent tries to maximise its summed discounted rewards over time, where discounting is used to avoid infinite utilities and encourage the agent to value current rewards more than future ones. Some commonly used discount…
The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individuals genomes are represented by bit-strings. It provides a simple metaphor for the evolutionary process in terms of the…
In this paper, we are concerned with the valuation of Guaranteed Annuity Options (GAOs) under the most generalised modelling framework where both interest and mortality rates are stochastic and correlated. Pricing these type of options in…
We study actuarial fairness in China's notional defined contribution (NDC) pension system when mortality differs across income groups. Under current rules, individual account balances are converted into monthly benefits using an official…
In this paper we summarize the main parts of the first exit time theory developed in connection to the life table data and the resulting theoretical and applied issues. Several new tools arise from the development of this theory and…
This paper addresses the problem of determining the optimal time for an individual to convert retirement savings into a lifetime annuity. The individual invests their wealth into a dividend-paying fund that follows the dynamics of a…
This paper proceeds an approximate calculation of ultimate time survival probability for bi-seasonal discrete time risk model when premium rate equals two. The same model with income rate equal to one was investigated in 2014 by Damarackas…
Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power-law instead of pure power-law for the CTRW model in characterizing the waiting time and jump…
We derive some rather general, but complicated, formulae to compute the survival function and the first passage time distribution of the $n^\text{th}$ coordinate of a many-body stochastic process in the presence of a killing barrier. First…
We investigate fractional sums of arithmetic functions over products of two or three integers, with emphasis on fixed greatest common divisors and multiplicative weights. Let $f$ be an arithmetic function satisfying $f(n) \ll n^\alpha$ for…
We develop a theory for pricing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified…
In recent years, a market for mortality derivatives began developing as a way to handle systematic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of…
We consider the insurance company as a physical system which is immersed in its environment (the financial market). The insurer company interacts with the market by exchanging the money through the payments for loss claims and receiving the…
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…