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oai:figshare.com:article/34007886 2026-09-28T04:23:06Z category_792 portal_316 item_type_3 month_year_09_2026

Supplementary file 1_A stochastic differential game between two hybrid pension fund managers under a jump-diffusion liability process.pdf Oteng Keganneng (25119153) Eriyoti Chikodza (25119156) Othusitse Basimanebotlhe (25119159) Applied Mathematics not elsewhere classified jump-diffusion liability Nash equilibrium pension fund stochastic differential game Background<p>Hybrid defined contribution (DC) pension funds, combining fixed contributions with stochastic liability dynamics, face competitive pressures when members reallocate contributions to higher-performing funds.</p>Methods<p>We model two competing hybrid DC pension fund managers in a stochastic differential game. Liability risk is modelled as a jump-diffusion process with truncated exponential jump amplitudes, using the exact asset-to-liability ratio formulation. The Hamilton–Jacobi–Bellman dynamic programming approach yields Nash equilibrium portfolio strategies and value functions in closed form.</p>Results<p>The Nash equilibrium portfolio weights are independent of liability jump parameters. In the symmetric liability-correlation case, they reduce to K = (μ−r)/σ², independent of both managers' risk aversion. In the asymmetric case, risk aversion enters through a cross-liability correction term. Competition strictly amplifies risk-taking relative to the single-agent benchmark. Liability jumps significantly affect welfare: a manager's own jumps reduce welfare while the competitor's jumps improve it.</p>Discussion<p>These results extend Nash equilibrium analysis for DC pension funds to jump-diffusion liabilities, showing that while jump parameters do not alter equilibrium portfolio strategies, they materially affect welfare through two loading functions capturing own-jump welfare costs and cross-player spillovers. Numerical illustrations confirm all theoretical predictions.</p> 2026-09-28T04:23:06Z Dataset Dataset 10.3389/fams.2026.1931310.s001 https://figshare.com/articles/dataset/Supplementary_file_1_A_stochastic_differential_game_between_two_hybrid_pension_fund_managers_under_a_jump-diffusion_liability_process_pdf/34007886 CC BY 4.0