Blanchet, J. and Lam, H. A Heavy Traffic Approach to Modeling Large Life Insurance Portfolios. Insurance: Mathematics and Economics, 53, (2013), 237-251.

Summary:

One of the first things you learn in a life insurance course is the concept of reserve. The reserve (from a prospective perspective) at any point in time equals the actuarial net present values of the benefits to be paid minus the premiums to be received. The paper tracks this process in time from bottom up, that is, aggregating customer by costumer. In the asymptotic regime in which there are many customers, a functional CLT is obtained. We characterize a limiting Gaussian process whose correlation structure is contract-dependent. We are able to recover the expected value of the reserve according to the standard formulae studied in practice, but also fluctuations around it. The results can be used to quantify, dynamically in time, if the company is in good shape and define sample-path risk measures (e.g. first passage time probabilities etc.)

Bibtex:

@Article{BL_2013,

author = {J. Blanchet and H. Lam},

title = {A heavy traffic approach to modeling large life insurance portfolios},

journal = {Insurance: Mathematics and Economics},

year = {2013},

volume = {53},

pages = {237-251}

}