The Process of the Household Financial Surplus with Incomplete Retirement and Fixed Consumption Needs

If consumption needs of a household are deterministic (except the stochastic factor of life-length) and a life-long financial plan allows for incomplete retirement, dynamics of a cumulated net cash flow (cumulated surplus) reflects a financial situation of the household in the best manner. The goal of the paper is to combine a two-person survival process with the expected discounted utility model, so that it suits Feldman, Pietrzyk and Rokita (2013) framework. This will constitute a theoretical basis for constructing an algorithm that will facilitate household financial plan optimization based on Monte Carlo method. The outcome of a financial plan is reflected by a set of term structures of cumulated surplus, corresponding to a set of scenarios. For a cumulated net cash flow model to be utilized as a tool for facilitating an optimization plan, it is required to capture and analyse the entire process, not just the expected trajectory. In a discrete version, all trajectories of the process may be generated. The article presents a proposal of their further use. This concept differs significantly from the traditional approach in which discounted utilities of consumption have been multiplied by the subsequent conditional probabilities of survival. That might function well for an individual for whom only two survival states (alive or not) are possible. In our proposal, each possible trajectory of the process is weighted with its unconditional probability. Such an approach seems to be much better tractable than any one with conditional probabilities applied to each moment on the timeline.