The Marginal Cost of Risk in a Multi-Period Risk Model

Capital allocation is used widely within the insurance industry for purposes of pricing and performance measurement. The practice, however, inspires controversy on several levels. Some question its necessity Phillips, Cummins, and Allen, 1998; Sherris, 2006). Others argue that it leads to economically suboptimal decisions (Venter, 2002; Grundl and Schmeiser, 2007). Many thought leaders in the actuarial community have picked up on this disparity providing various vantage points why the allocation problem may be misguided or what the debate may be missing (Mango, 2005; Kreps, 2005; Venter, 2010; D'Arcy, 2011).

In this report, we start in Chapter 2 by reviewing the various approaches to capital allocation and identifying the circumstances under which pricing based on capital allocation is economically optimal. To preview, in relatively simple settings, where the objective is to maximize firm value in a single period, capital allocation can be consistent with marginal cost pricing. This results trivially if the problem is cast as expected profit maximization subject to a risk measure constraint (in which case gradient allocation methods applied to the constraining risk measure are appropriate for pricing purposes). It also results in more complex specifications of the single period model, although the correct risk measure is similarly complex (Bauer and Zanjani, 2013a).

Keywords: capital allocation, risk measures