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Most insurance contracts are inherently linked to financial markets, be it via interest rates, or -- as hybrid products like equity-linked life insurance and variable annuities -- directly to stocks or indices. However, insurance contracts are not for trade except sometimes as surrender to the selling office. This excludes the situation of arbitrage by buying and selling insurance contracts at different prices. Furth…
Designing dynamic portfolio insurance strategies under market conditions switching between two or more regimes is a challenging task in financial economics. Recently, a promising approach employing the value-at-risk (VaR) measure to assign weights to risky and riskless assets has been proposed in [Jiang C., Ma Y. and An Y. "The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis" , Inte…
In most cases, insurance contracts are linked to the financial markets, such as through interest rates or equity-linked insurance products. To motivate an evaluation rule in these hybrid markets, Artzner et al. (2022) introduced the notion of insurance-finance arbitrage. In this paper we extend their setting by incorporating model uncertainty. To this end, we allow statistical uncertainty in the underlying dynamics t…
We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance, i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) of an insurance company with the amount of claims described by the risk model based on GCHP. The novelty of the results consists of the new Hawkes-…
We determine how an individual can use life insurance to meet a bequest goal. We assume that the individual's consumption is met by an income, such as a pension, life annuity, or Social Security. Then, we consider the wealth that the individual wants to devote towards heirs (separate from any wealth related to the afore-mentioned income) and find the optimal strategy for buying life insurance to maximize the probabil…
In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer's theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance sampling are used in rare event simulation for option pricing. We finally focus on large deviations m…
This paper aims to extend downside protection to a hedge fund investment portfolio based on shared loss fee structures that have become increasing popular in the market. In particular, we consider a second tranche and suggest the purchase of an upfront reinsurance contract for any losses on the fund beyond the threshold covered by the first tranche, i.e. gaining full portfolio protection. We identify a fund's underly…
We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading app…
Climate perils are linked through event ordering and state-dependent propagation, features not fully captured by joint loss distributions alone. This paper develops a Cascading Climate Risk Network (CCRN) for multi-peril reinsurance that separates calendar-scale climate conditioning from within-event propagation on a directed acyclic graph (DAG). The model combines complementary-log-log triggering hazards with bounde…
AI losses that arise through an insured organization's generative or agentic AI system require state reconstruction, not merely event reconstruction, because the relevant state changes as the system reasons, retrieves, calls tools, and acts. The relevant question is not only what loss occurred, but what the system was allowed to do, what it actually did, and whether that reconstructed loss can support insurance claim…
Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space a…
Modelling claim frequency and severity for non-life insurance pricing predominantly relies on generalised linear models, with gradient-boosted machines as the leading machine learning alternative. Tabular foundation models (TFMs) present a fundamentally different inference paradigm. By pre-training on large collections of synthetic datasets, TFMs enable inference on new data through in-context learning, without any d…
Capped-usage SaaS products -- LLM subscriptions such as Claude Code and ChatGPT, cloud platforms such as Vercel and Cloudflare Workers, corporate benefit platforms, identity-verification services with liability transfer -- share a structural signature with insurance products: a fixed premium decoupled from realized consumption, stochastic per-user demand with heavy-tailed severity, a non-fungible cap that resets on a…
This work evaluates the impact of contagious cyber-events, over a finite horizon, on firms' financial health and on a cyber insurance portfolio. Our approach builds on key empirical findings from economics and cybersecurity. In economics, firm size and growth-rate distributions are non-Gaussian and exhibit heavy tails. In cybersecurity, contagion dynamics strongly depend on firm size and environmental conditions. To …
We formulate a dynamic reinsurance problem in which the insurer seeks to control the terminal distribution of its surplus while minimizing the L2-norm of the ceded risk. Using techniques from martingale optimal transport, we show that, under suitable assumptions, the problem admits a tractable solution analogous to the Bass martingale. We first consider the case where the insurer wants to match a given terminal distr…
Given the increasing importance of environmental, social and governance (ESG) factors, particularly carbon emissions, we investigate optimal proportional portfolio insurance (PPI) strategies accounting for carbon footprint reduction. PPI strategies enable investors to mitigate downside risk while retaining the potential for upside gains. This paper aims to determine the multiplier of the PPI strategy to maximise the …
This paper studies systemic-risk connectedness in the European insurance sector at three levels of granularity: across major segments of financial markets, across insurance subsectors, and across individual insurance companies. Using a common connectedness framework applied to returns, volatility, value-at-risk, and expected shortfall, we document that insurers are an important component of systemic-risk connectednes…
In economic analysis, rational decision-makers often take actions to reduce their risk exposure. These actions include purchasing market insurance and implementing prevention measures to modify the shape of the loss distribution. Under the assumption that the insureds' actions are fully observed by the insurer, this paper investigates the interaction between self-protection and insurance demand when insurance premium…
Deposit insurance is a public guarantee on eligible deposits up to a cap — a run-stopper that creates moral hazard and a hard cap problem.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
A protective put is long the asset and long a put — a floor under the position for a premium that bleeds.
Moral hazard is hidden action after a contract is signed: insurance, a guarantee, or a backstop changes the agent’s incentives and often raises the risk the principal wanted to cover.
Black Monday (19 October 1987) was a one-day ~22% crash in the DJIA, amplified by portfolio insurance — a mechanical selling program that turned a decline into a gap.
Cyprus 2013 combined a Greek-PSI hole in bank assets with a huge banking system versus GDP and ended in bail-in, capital controls, and a depositor haircut above insurance — a euro-area first.
The law of large numbers says the sample average converges to the expected value as n grows — the reason insurance and a large independent bet-set work, and a small correlated book does not.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.
Black Monday (19 October 1987) was a one-day ~22% crash in the DJIA, amplified by portfolio insurance — a mechanical selling program that turned a decline into a gap.
A CDS is a bilateral contract that pays the loss on a reference credit after a credit event — default insurance quoted as a spread.
Cyprus 2013 combined a Greek-PSI hole in bank assets with a huge banking system versus GDP and ended in bail-in, capital controls, and a depositor haircut above insurance — a euro-area first.
Deposit insurance is a public guarantee on eligible deposits up to a cap — a run-stopper that creates moral hazard and a hard cap problem.
The law of large numbers says the sample average converges to the expected value as n grows — the reason insurance and a large independent bet-set work, and a small correlated book does not.
Moral hazard is hidden action after a contract is signed: insurance, a guarantee, or a backstop changes the agent’s incentives and often raises the risk the principal wanted to cover.
Sell implied volatility and buy realized — harvest the gap that insurance buyers pay, with a jump left tail.