Abstract: This study explores the optimal risk diversification for a reinsurer that manages two separate stop-loss contracts with two distinct insurers. A practical stochastic framework is introduced, utilizing the Heston model to approximate the distribution of aggregate claims generated by two correlated processes. The core of the analysis involves determining the optimal barrier levels (retention and cap) for these contracts. This optimization is designed to meet two criteria: ensuring fair cost-sharing between the reinsurer and the primary insurers, and minimizing the expected cost differences for the reinsurer. The numerical results highlight the significant role of claim correlation and various contract parameters in achieving optimal risk-sharing and equitable cost allocation. This research provides both theoretical insights and practical guidance for designing modern reinsurance mechanisms by incorporating stochastic volatility into a multi-insurer contract structure.

Abstract: We give a complete solution to an open problem by using the spectral method on the polynomial generator matrices of quasicyclic codes of an arbitrary index, with the corresponding reduced Gröbner basis of the given quasi-cyclic code. To be more specific, we construct a full generator matrix over a suitable extension field of the given base field using this method. For indices 2 and 3, we demonstrate two respective examples to show how we construct the full generator matrix from the given polynomial generator matrix. Moreover, we show that the reduced Gröbner basis of the subclass of 2D-cyclic codes should provide a polynomial generator matrix in diagonal form in the cases of index 2 and index 3.

Abstract: Accurate inflation forecasting is essential for policymakers, businesses, and households because it shapes budgeting, monetary policy decisions, investment planning, wage setting, and overall economic stability. Yet inflation is difficult to predict due to the combined effects of monetary and fiscal policies, global conditions, shocks, and geopolitical risks. This study proposes a dynamic multinomial framework designed to capture both the underlying structure of macroeconomic data and the evolving regimes that drive inflation dynamics. The model integrates fuzzy logic with principal component analysis to create Fuzzy-Inferred PCA (FIPCA), a dimensionality reduction method that represents uncertainty and nonlinear interactions among macroeconomic variables. This produces a condensed time series that more effectively summarizes the broader economic environment compared to traditional PCA. This macroeconomic indicator is then used within a Hierarchical Hidden Markov Model that identifies long-term economic regimes and produces state probabilities reflecting shifts in inflation behavior. These regimes guide a stochastic process based on Geometric Brownian Motion, allowing inflation paths to evolve according to changing economic conditions rather than fixed parameters. Regime-specific parameters are estimated using data subsets aligned with the identified states, providing a flexible structure that adapts to transitions in the economy. The resulting hybrid framework demonstrates that combining fuzzy-enhanced dimensionality reduction, regime identification, and state-dependent stochastic modeling can improve the accuracy and reliability of inflation forecasting in environments subject to structural change and uncertainty.

Abstract: Climate anomalies pose significant threats to agricultural productivity and food security by severely disrupting crop yields. This study models annual crop yields across U.S. states by incorporating extreme weather covariates, specifically the components of the Actuaries Climate Index, which has gained recent popularity in climate-related risk applications. To capture the dynamic interdependence among weather variables, we use copula models. The resulting copula-based dependence parameters are subsequently integrated into a class of stochastic differential equations, enabling  dynamic quantification of climate effects on crop yield outcomes.

Abstract: In this study, we solve exit problems for a level-dependent Lévy processes which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All identities are given in terms of new generalisations of scale functions (counterparts of the scale function from the theory of  Lévy processes), which are solutions of Volterra integral equations. Furthermore, we obtain similar results for the reflected level-dependent  Lévy processes. The existence of the solution of the stochastic differential equation for reflected level-dependent L´evy processes is also discussed. Finally, to illustrate our result the probability of bankruptcy is obtained for an insurance risk process.

Abstract: Private Information Retrieval (PIR) scheme aims to retrieve data from a database without revealing any details about the identity of the data. The PIR scheme for coded storage systems with colluding servers gives a better PIR rate when the storage code and retrieval code have transitive automorphism groups. In this work, we study the transitivity of nD-cyclic codes and then PIR schemes from them together with several examples of nD-cyclic codes with better PIR rates. Then, we show the monomial equivalence between nD-cyclic codes and certain nD-constacyclic codes, which can be used as an alternative family of transitive codes.