Arbitrage‑free catastrophe reinsurance valuation for compound dynamic contagion claims
                             
                                            
                                                    
                            
                The insurance sector faces pressure from rising catastrophic risks, leading to higher premiums and policy non-renewals. This paper proposes an arbitrage-free method for pricing catastrophe reinsurance using the compound dynamic contagion process and Esscher transform. The findings help insurers assess liabilities amid emerging risks like climate change, cyberattacks, and pandemics.