The Optimal Decision Strategy in the Second Pillar of the Slovak Pension System

The aim of this study is to determine and analyse the optimal investment strategy that faces any participant of the defined-contributions based private scheme of Slovak pension system when deciding about the proper pension fund selection combining two pension funds Index Fund and Bond Fund - that would lead to the maximal possible expected future income. We formulate this problem of optimal risk-sensitive dynamic portfolio construction in terms of the Hamilton-Jacobi-Bellman equation, approximate its solution employing double asymptotic and provide the solution qualitative and quantitative analysis. The key message of our study is a general advice for an average participant of the Second Pillar: it is optimal to allocate the wealth into the Index Fund for the first 3/4 of accumulation period and then gradually move towards the Bond Fund. The allocated wealth can be considerably increased by raise in contribution rate and/or liberated legislative restrictions.