Derives measure changes for pricing midcurve swaptions.
problem Pricing midcurve swaptions in a forward swap annuity measure.
method Derives measure change formulae and constructs linear and exponential terminal swap rate models.
result Captures midcurve swaption correlation skew.
Global existence of equilibrium in incomplete market with stochastic annuity.
problem Proving existence of equilibrium in an incomplete market with stochastic annuity.
method Characterized by fully coupled quadratic backward stochastic differential equations, existence proved under Markovian assumptions.
result Global existence of an incomplete, continuous-time finite-agent Radner equilibrium.
Paper presents deep LSMC method for efficient variable annuity pricing.
problem Efficiently pricing variable annuities with guarantees using simulation methods.
method Modifies least-squares Monte Carlo (LSMC) algorithm for optimal stochastic control problems.
result Deep LSMC provides more stable and robust pricing performance for higher-dimensional problems.
The paper analyzes GMWB annuities in low interest rate environments.
problem Valuation of GMWB annuities in low interest rate conditions.
method Dynamic programming and Hull-White interest rate model.
result Low interest rates increase the fair value of GMWB annuities.
This paper examines how taxation and stochastic interest rates affect GMWB Variable Annuities.
problem Improving the financial cost and withdrawal dynamics of GMWB Variable Annuities.
method Developed a numerical framework to compute fair value of GMWB contracts, accounting for taxation and stochastic interest rates.
result Accounting for both taxation and stochastic interest rate significantly impacts GMWB withdrawal strategy and cost.
Enhances valuation of variable annuities with stochastic interest rate models.
problem Valuation and optimal surrender strategies for variable annuities in Lévy models.
method Hybrid numerical method combining tree methods for interest rate modeling and finite difference techniques for asset price.
result Influence of stochastic interest rates on surrender decisions and contract design.
The paper uses GPR to speed up pricing of GMWB VA with stochastic vol and rate.
problem Pricing and computing Greeks of GMWB VA with stochastic vol and rate.
method Gaussian Process Regression for numerical solution of dynamic control problem.
result GPR significantly speeds up computation with high accuracy.
The paper provides bounds for pricing Guaranteed Annuity Options under stochastic interest and mortality rates.
problem Valuation of Guaranteed Annuity Options in a correlated stochastic environment.
method Employing doubly stochastic stopping times and a change of measure, the authors derive general price bounds for GAOs.
result Derivation of general price bounds for GAOs using a conditioning approach for the lower bound and arithmetic-geometric mean inequality for the upper bound.
The paper values variable annuities using complex stochastic models and deep learning.
problem Valuation of variable annuities with early surrender options under non-Markovian models.
method Developed a deep signature Least Squares Monte Carlo approach to handle path-dependent continuation values.
result Fair fees increase with Hurst parameters of stock volatility and mortality force.
Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.
problem Pricing equity-indexed annuities with early surrender risk under uncertain market conditions.
method Advanced financial modeling techniques, including uncertain volatility framework and Hull-White model for interest rate dynamics. Numerical algorithm using tree-based framework with local volatility optimization.
result High effectiveness of the proposed numerical algorithm compared to machine learning-based methods.
Proposes GLWB-LTC for enhanced life care annuities with dynamic withdrawal strategies and stochastic interest rates.
problem Improving life care annuity features and pricing methods.
method Introduces GLWB-LTC with dynamic withdrawal strategies and stochastic interest rates. Solves the stochastic control problem using a robust tree method.
result Optimal withdrawal strategies vary over time with policyholder's health status, highlighting the advantage of flexibility.
In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatil…
Study proposes a new model for joint survival annuity valuation.
problem Valuation of joint survival annuities and options.
method Linear-rational Wishart mortality model based on stochastic matrix affine process.
result Derives closed-form expression for joint survival annuity and option.
This paper examines the optimal annuitization, investment and consumption strategies of a utility-maximizing retiree facing a stochastic time of death under a variety of institutional restrictions. We focus on the impact of aging on the optimal purchase of life annuities which form the basis of most Defined Benefit pen…
In this article we investigate a state-space representation of the Lee-Carter model which is a benchmark stochastic mortality model for forecasting age-specific death rates. Existing relevant literature focuses mainly on mortality forecasting or pricing of longevity derivatives, while the full implications and methods …
In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behaviour solved as an optimal stochastic control problem. This product simultaneously deals with financial risk, mortali…
This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap. Although swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, also provide downside protection. A tractable stochastic mortality model with age dependent …
We consider a large, homogeneous portfolio of life or disability annuity policies. The policies are assumed to be independent conditional on an external stochastic process representing the economic-demographic environment. Using a conditional law of large numbers, we establish the connection between claims reserving an…
In this paper, we review pricing of variable annuity living and death guarantees offered to retail investors in many countries. Investors purchase these products to take advantage of market growth and protect savings. We present pricing of these products via an optimal stochastic control framework, and review the exist…
Hedging methods to mitigate the exposure of variable annuity products to market risks require the calculation of market risk sensitivities (or "Greeks"). The complex, path-dependent nature of these products means these sensitivities typically must be estimated by Monte Carlo simulation. Standard market practice is to m…
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
Study analyzes fees linked to VIX index in annuity contracts.
problem Impact of VIX-linked fees on annuity contract surrender strategies.
method Two-layer continuous-time Markov chain approximation for fund value process.
result Optimal surrender strategy is more robust to VIX-linked fees.
We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a reversible life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and t…
Paper solves annuity pricing puzzle by minimizing risk.
problem Inconsistency between theory and empirical observations in annuities pricing.
method Risk minimization approach to price annuities for both producer and customer.
result Different pricing solutions for annuity price and rate of payments.
Paper proposes decentralized annuities for better retirement security.
problem Current pension systems' limitations and fairness issues.
method Theoretical models and fairness concepts analysis.
result Decentralized annuities offer enhanced flexibility and social welfare.
We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and can purchase a deferred annuity. Although we let the admissible set of strategies of annuity purchasing process to be increasing adapted processes, we find that the individual will not buy a …
Optimizes investment and consumption for post-retirement with minimum guarantee.
problem Maximizing final annuity with minimum guarantee during decumulation phase.
method Dynamic programming via Hamilton-Jacobi-Bellman (HJB) equation, finite difference method.
result Existence and uniqueness of classical solutions proved through dual transformation.
Investigates optimal life insurance and annuity decisions in inflationary economies.
problem Optimal consumption and investment decisions in an inflationary economy with money illusion.
method Formulated as a random horizon utility maximization problem, derived optimal strategy.
result Money illusion increases life insurance demand for young adults and reduces annuity demand for retirees.
The paper studies optimal annuity purchase timing under uncertain mortality forces.
problem Optimal timing to purchase an annuity with uncertain mortality forces.
method Formulated as a real option, probabilistic study with new solution methods.
result Detailed probabilistic study of the optimal stopping boundary.
Insurance companies often include very long-term guarantees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (G.A.O), the insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rated when the policy matures. Both …
The paper examines variable annuities pricing and risk management using the Black-Scholes model and identifies key risk drivers.
problem Model risk in pricing and managing variable annuities using the Black-Scholes model.
method Derives a model-free decomposition of variable annuity prices and investigates hedging strategies.
result The spot price risk can always be eliminated by the BS-based hedging strategy, but there is gradual slippage and instantaneous leakage.
The paper offers a new model for variable annuities with surrender risk.
problem Modeling variable annuities with surrender risk and market consistency.
method Hybrid model with Lévy processes, time-inhomogeneous, and dependence between financial and surrender risks.
result Explicit analytical formulas and practical numerical procedures for variable annuity valuation.
Optimal timing for converting savings into annuities considering mortality risk.
problem Determining the best time to annuitize retirement savings under stochastic mortality.
method Formulated as a three-dimensional optimal stopping problem, reduced to nested one-dimensional problems, solved using PDMP structure.
result Rich structure for the optimal annuitization rule, covering various parameter specifications.
Paper assesses GMMB in VAs using FST for accurate net liability calculations.
problem Risk management of GMMB under stochastic mortality and regime-switching.
method Net liability model with FST algorithm for accurate numeric solutions.
result FST algorithm provides reliable results for net liability of GMMB.
Analyzes how many people can receive stable income in a pooled annuity fund.
problem Quantifying the trade-off between income stability and the number of members in a pooled annuity fund.
method Investment returns held constant, systematic longevity risk omitted. Derived an analytical expression for income stability.
result The number of fund members who receive stable income is independent of the mortality model.
Existence of Radner equilibrium proven with growing population.
problem Analyzing Radner equilibrium in a model with population growth.
method Proved existence of equilibrium for growing population using mathematical analysis.
result Equilibrium exists for a growing population, with effects on annuity prices.
Research examines GMIB and reset options in variable annuities.
problem Understanding the value and rationality of GMIB and reset options.
method Exploration of various parameters affecting GMIB value and calculation of critical future interest rates for reset option rationality.
result Insight into how future market performance and interest rates influence policyholder and insurer actions.
Examines how longevity risk pooling affects retirees' valuation of annuities.
problem Determines if and how retirees benefit from pooling longevity risk.
method Combines economics of annuity equivalent wealth with actuarial models of aging.
result Retirees with higher relative mortality place higher value on annuities.
Refundable income annuities offer a money-back guarantee, now the majority of sales.
problem The complexity and market neglect of refundable income annuities.
method Explained the pricing, duration, and money's-worth-ratio of refundable IAs, proving a counterintuitive price behavior.
result The market price of cash-refund IAs is not a declining function of age, and older buyers might pay more than younger ones.
Historical tontines promised enormous rewards to the last survivors at the expense of those who died early. While this design appealed to the gambling instinct, it is a suboptimal way to manage longevity risk during retirement. This is why fair life annuities making constant payments -- where the insurance company is e…
Study on pooled annuity funds and how initial savings affect income stability.
problem Analyzing the stability of income payments in pooled annuity funds.
method Examining the influence of initial savings on income fluctuations and developing a criterion for pooling funds.
result Identification of a term, the 'implied number of homogeneous members', linking initial savings to income fluctuations.
A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder,…
We develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of…
The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.
problem Analyzing Variable Annuities with surrender charges and early termination rights.
method Formulated as an optimal stopping problem with a discontinuous payoff, non-monotonic optimal stopping boundaries are proven continuous and regular.
result A rigorous pricing formula and optimal exercise boundary for surrender options are derived.
Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) is an optimal stochastic control problem. The surrender feature available in marketed products allows termination of the contract before maturity, making it also an optimal stoppi…
The paper evaluates dynamic hedging strategies for various financial products.
problem Pricing derivative products with dynamic hedging and issuer-tailored risk.
method Unified constrained discrete stochastic dynamic programming framework with sequential local minimizing strategies.
result Demonstrates flexibility of the unified framework through numerical examples.
Paper uses Gibbs sampler with jump diffusion for European option pricing.
problem Estimating market parameters for jump diffusion models in option pricing.
method Gibbs sampler applied to jump diffusion model for estimating drift, volatility, jump intensity, and occurrence.
result Demonstrates impact of jump effects on European call option and annuity pricing.
Paper proposes a deep RL method for hedging variable annuities, outperforming misspecified models.
problem Model miscalibration in variable annuity contracts with GMMB and GMDB riders.
method Two-phase deep reinforcement learning approach: training phase in a controlled environment, online learning phase in real market.
result Trained reinforcement learning agent hedges equally well as correct Delta in training phase and outperforms misspecified Deltas.