In this paper we construct a dynamic entry deterrence game in which market demand follows the Chan-Karolyi-Longstaff-Sanders (CKLS) stochastic differential equation (SDE). The incumbent firm, whose true strength is privately known, uses advertising and promotional expenditures strategically to shape the entrant’s beliefs. On the other hand, the entrant, facing a costly and irreversible decision, delays entry until demand reaches a critical level, with outcomes depending on both the incumbent’s hidden type and uncertain demand. Under this dynamic Stackelberg environment by implementing a path integral control approach, we determine a Markovian Nash feedback equilibrium. We also performed an empirical study based on revenue data from Enterprise Products Partners and Targa Resources over the period 2010-2024, and the resulting empirical findings are consistent with the theoretical predictions of the proposed model. The empirical trajectories exhibit qualitative patterns that are consistent with the mechanisms emphasized by the theoretical model, particularly with respect to persistence, recovery following adverse shocks, and differences in the responses of firms occupying distinct competitive positions.
M. Issah, Paramahansa Pramanik· SN Business & Economics· 0 citations
In this paper we construct a dynamic entry deterrence game in which market demand follows the Chan-Karolyi-Longstaff-Sanders (CKLS) stochastic differential equation (SDE). The incumbent firm, whose true strength is privately known, uses advertising and promotional expenditures strategically to shape the entrant’s beliefs. On the other hand, the entrant, facing a costly and irreversible decision, delays entry until demand reaches a critical level, with outcomes depending on both the incumbent’s hidden type and uncertain demand. Under this dynamic Stackelberg environment by implementing a path integral control approach, we determine a Markovian Nash feedback equilibrium. We also performed an empirical study based on revenue data from Enterprise Products Partners and Targa Resources over the period 2010-2024, and the resulting empirical findings are consistent with the theoretical predictions of the proposed model. The empirical trajectories exhibit qualitative patterns that are consistent with the mechanisms emphasized by the theoretical model, particularly with respect to persistence, recovery following adverse shocks, and differences in the responses of firms occupying distinct competitive positions.
M. Issah, Paramahansa Pramanik· SN Business & Economics· 0 citations
We study dynamic physical hedging for insurers exposed jointly to catastrophe losses and stochastic reconstruction costs. Surplus evolves as a controlled jump diffusion whose loss amplitude combines marked catastrophe severity, an exogenous mean-reverting cost factor, and endogenous mitigation. We establish well-posedness, moment and stability estimates, and a stopping-time dynamic programming principle, and prove that the value function is the unique viscosity solution of the resulting nonlocal Hamilton-Jacobi-Bellman (HJB) equation Strategic interaction is introduced through a mean field game (MFG) with reduced-form vulnerability costs, yielding a coupled backward-forward HJB-Kolmogorov system. We establish relaxed equilibrium existence, Markovian realization, and uniqueness under appropriate compactness and monotonicity conditions. Numerical experiments show that reconstruction costs and capitalization materially affect optimal hedging and that cross-sectional vulnerability alters equilibrium costs. Tail-family robustness calculations further assess the sensitivity of these conclusions to alternative catastrophe-severity specifications.
Paramahansa Pramanik, Michael Bowdin· 0 citations
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