On (P,Q )-Binomial Extension of Cox-Ross-Rubinstein Model for Optimization of Portfolio with Noisy Observations in Life Insurance

Abstract

In the realm of dynamic life insurance portfolio management, enhanc- ing the Cox-Ross-Rubinstein (CRR) model becomes imperative amid the challenges presented by noisy observations. This quest arises from a nu- anced understanding of the intricacies involved in modeling life insurance portfolios, particularly in the presence of uncertainties and fluctuations represented by noisy observations. An augmentation of the CRR model is undertaken through a(p, q)-binomial framework introducing a novel pa- rameter p. The objectives of this study are to; Develop a (p,q)-extension of CRR model with noisy observations; Establish optimization condi- tions for the extended model with noisy observations and Simulate the outcomes of the model in life insurance. The (p, q)-binomial distribu- tion facilitates a (p, q)-random walk within the CRR model, aligning it with the Black-Scholes model. Our approach includes developing a util- ity function for investor preference analysis, examining noise sensitivity, and establishing constraints for structured optimization. Practical sim- ulations of the extended model in life insurance contexts demonstrates the model’s real-world applicability. The study’s innovative approach to integrating noisy market data into the model is intended to facilitate the strategic modeling of optimal portfolios, while judiciously balancing risk considerations. Furthermore the study delves into a more mathematical exploration of the model’s sensitivity and responsiveness to various mar- ket conditions. Future research could focus on enhancing the precision of the model by incorporating advanced mathematical techniques, such as stochastic calculus or machine learning algorithms, to better predict and optimize portfolio performance amidst market uncertainties.