arXiv subjects

Cody Hyndman

Publications and source records attributed to Cody Hyndman.

12 recordsLinked to original sources

arXiv2026

Habit Formation, Labor Supply, and the Dynamics of Retirement and Annuitization

The decision to annuitize wealth in retirement planning has become increasingly complex due to rising longevity risk and changing retirement patterns, including increased labor force participation at older ages. While an extensive literature studies consumption, labor, and annuitization decisions, these elements are typically examined in isolation. This paper develops a unified stochastic control and optimal stopping framework in which habit formation and endogenous labor supply shape retirement and annuitization decisions under age-dependent mortality. We derive optimal consumption, labor, portfolio, and annuitization policies in a continuous-time lifecycle model. The solution is characterized via dynamic programming and a Hamilton-Jacobi-Bellman variational inequality. Our results reveal a rich sequence of retirement dynamics. When wealth is low relative to habit, labor is supplied defensively to protect consumption standards. As wealth increases, agents enter a work-to-retire phase in which labor is supplied at its maximum level to accelerate access to retirement. Human capital acts as a stabilizing asset, justifying a more aggressive pre-retirement investment portfolio, followed by abrupt de-risking upon annuitization. Subjective mortality beliefs are a key determinant in shaping retirement dynamics. Agents with pessimistic longevity beliefs rationally perceive annuities as unattractive, leading them to avoid or delay annuitization. This framework provides a behavior-based explanation for low annuity demand and offers guidance for retirement planning jointly linking labor supply, portfolio choice, and the timing of annuitization.

q-fin.MF↗

arXiv2025

Boundary error control for numerical solution of BSDEs by the convolution-FFT method

We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the boundary errors obtained when valuing options using this approach. We modify the damping and shifting schemes used in the original formulation, which transforms the target function into a bounded periodic function so that Fourier transforms can be applied successfully. Time-dependent shifting reduces boundary error significantly. We present numerical results for our implementation and provide a detailed error analysis showing the improved accuracy and convergence of the modified convolution method.

math.NA↗

arXiv2025

Convolution-FFT for option pricing in the Heston model

We propose a convolution-FFT method for pricing European options under the Heston model that leverages a continuously differentiable representation of the joint characteristic function. Unlike existing Fourier-based methods that rely on branch-cut adjustments or empirically tuned damping parameters, our approach yields a stable integrand even under large frequency oscillations. Crucially, we derive fully analytical error bounds that quantify both truncation error and discretization error in terms of model parameters and grid settings. To the best of our knowledge, this is the first work to provide such explicit, closed-form error estimates for an FFT-based convolution method specialized to the Heston model. Numerical experiments confirm the theoretical rates and illustrate robust, high-accuracy option pricing at modest computational cost.

q-fin.CP↗

arXiv2025

Arbitrage-Free Bond and Yield Curve Forecasting with Neural Filters under HJM Constraints

We develop an arbitrage-free deep learning framework for yield curve and bond price forecasting based on the Heath-Jarrow-Morton (HJM) term-structure model and a dynamic Nelson-Siegel parameterization of forward rates. Our approach embeds a no-arbitrage drift restriction into a neural state-space architecture by combining Kalman, extended Kalman, and particle filters with recurrent neural networks (LSTM/CLSTM), and introduces an explicit arbitrage error regularization (AER) term during training. The model is applied to U.S. Treasury and corporate bond data, and its performance is evaluated for both yield-space and price-space predictions at 1-day and 5-day horizons. Empirically, arbitrage regularization leads to its strongest improvements at short maturities, particularly in 5-day-ahead forecasts, increasing market-consistency as measured by bid-ask hit rates and reducing dollar-denominated prediction errors.

q-fin.MF↗

arXiv2025

Optimal annuitization with labor income under age-dependent force of mortality

We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases with wealth until a threshold set by labor supply. After retirement, agents tend to consume a larger portion of their wealth. Two main factors influence optimal annuitization decisions as people get older. First, the agent's perspective (demand side); the agent's personal discount rate rises with age, reducing their desire to annuitize. Second, the insurer's perspective (supply side); insurers offer higher payout rates (mortality credits). Our model demonstrates that beyond a certain age, sharply declining survival probabilities make annuitization substantially optimal, as the powerful incentive of mortality credits outweighs the agent's high personal discount rate. Finally, post-retirement labor income serves as a direct substitute for annuitization by providing an alternative stable income source. It enhances the financial security of retirees.

q-fin.PM↗

arXiv2023

Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of Kratsios and Papon (2022) solves this problem without having prior assumptions on the market's "clipped" log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.

q-fin.CP↗

arXiv2022

A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In addition to suppressing extrapolation error, leading to a globally convergent numerical solution for the FBSDE, we provide explicit convergence rates. On this alternative grid the conditional expectations involved in the time discretization of the BSDE are computed using Fourier analysis and the fast Fourier transform (FFT) algorithm. The method is then extended to higher-order time discretizations of FBSDEs. Numerical results demonstrating convergence are presented using a commodity price model, incorporating seasonality, and forward prices.

q-fin.CP↗

arXiv2022

Optimal annuitization post-retirement with labor income

Evidence shows that the labor participation rate of retirement age cohorts is non-negligible, and it is a widespread phenomenon globally. In the United States, the labor force participation rate for workers age 75 and older is projected to be over 10 percent by 2026 as reported by the Bureau of Labor Statistics. The prevalence of post-retirement work changes existing considerations of optimal annuitization, a research question further complicated by novel factors such as post-retirement labor rates, wage rates, and capacity or willingness to work. To our knowledge, this poses a practical and theoretical problem not previously investigated in actuarial literature. In this paper, we study the problem of post-retirement annuitization with extra labor income in the framework of stochastic control, optimal stopping, and expected utility maximization. The utility functions are of the Cobb-Douglas type. The martingale methodology and duality techniques are employed to obtain closed-form solutions for the dual and primal problems. The effect of labor income is investigated by exploiting the explicit solutions and Monte-Carlo simulation. The latter reveals that the optimal annuitization time is strongly linear with respect to the initial wealth, with or without labor income. When it comes to optimal annuitization, we find that the wage and labor rates may play opposite roles. However, their impact is mediated by the leverage ratio.

q-fin.PM↗

arXiv2021

NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation

Effective feature representation is key to the predictive performance of any algorithm. This paper introduces a meta-procedure, called Non-Euclidean Upgrading (NEU), which learns feature maps that are expressive enough to embed the universal approximation property (UAP) into most model classes while only outputting feature maps that preserve any model class's UAP. We show that NEU can learn any feature map with these two properties if that feature map is asymptotically deformable into the identity. We also find that the feature-representations learned by NEU are always submanifolds of the feature space. NEU's properties are derived from a new deep neural model that is universal amongst all orientation-preserving homeomorphisms on the input space. We derive qualitative and quantitative approximation guarantees for this architecture. We quantify the number of parameters required for this new architecture to memorize any set of input-output pairs while simultaneously fixing every point of the input space lying outside some compact set, and we quantify the size of this set as a function of our model's depth. Moreover, we show that no deep feed-forward network with commonly used activation function has all these properties. NEU's performance is evaluated against competing machine learning methods on various regression and dimension reduction tasks both with financial and simulated data.

stat.ML↗

arXiv2019

The Entropic Measure Transform

We introduce the entropic measure transform (EMT) problem for a general process and prove the existence of a unique optimal measure characterizing the solution. The density process of the optimal measure is characterized using a semimartingale BSDE under general conditions. The EMT is used to reinterpret the conditional entropic risk-measure and to obtain a convenient formula for the conditional expectation of a process which admits an affine representation under a related measure. The entropic measure transform is then used provide a new characterization of defaultable bond prices, forward prices, and futures prices when the asset is driven by a jump diffusion. The characterization of these pricing problems in terms of the EMT provides economic interpretations as a maximization of returns subject to a penalty for removing financial risk as expressed through the aggregate relative entropy. The EMT is shown to extend the optimal stochastic control characterization of default-free bond prices of Gombani and Runggaldier (Math. Financ. 23(4):659-686, 2013). These methods are illustrated numerically with an example in the defaultable bond setting.

q-fin.MF↗

arXiv2016

Trading against disorderly liquidation of a large position under asymmetric information and market impact

We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liquidation trigger mechanism and the market impact. We classify these market participants into three types: fully informed, partially informed and uninformed investors. We consider the portfolio optimization problems and compare the optimal trading and wealth processes for the three classes of investors theoretically and by numerical illustrations.

q-fin.TR↗

arXiv2014

Explicit solutions of quadratic FBSDEs arising from quadratic term structure models

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are naturally related to similar results on affine term structure models of Hyndman (Math. Financ. Econ. 2(2):107-128, 2009) due to the relationship between quadratic functionals of Gaussian processes and linear functionals of affine processes. Similar to the affine case a sufficient condition for the explicit solutions to hold is the solvability in a fixed interval of Riccati-type ordinary differential equations. However, in contrast to the affine case, these Riccati equations are easily associated with those occurring in linear-quadratic control problems. We also consider quadratic models for a risky asset price and characterize the futures price and forward price of the asset in terms of similar FBSDEs. An example is considered, using an approach based on stochastic flows that is related to the FBSDE approach, to further emphasize the parallels between the affine and quadratic models. An appendix discusses solvability and explicit solutions of the Riccati equations.

q-fin.MF↗