arXiv subjects

Junkee Jeon

Publications and source records attributed to Junkee Jeon.

17 recordsLinked to original sources

arXiv2026

Finite-horizon Optimal Consumption and Investment with Costly Income Adjustment

We study optimal consumption and investment for an investor who receives labor income until a fixed retirement date, can raise the income rate irreversibly at a constant price per unit of income flow, and cannot borrow against future income. A pathwise argument shows that no income is purchased during a final period before retirement whose length depends only on the interest rate and the price. Before this period the dual problem has two free boundaries: a lower one generated by the borrowing constraint and an upper one, at which income is purchased, that escapes to infinity as the final period begins. The analysis of this problem is our main mathematical contribution. During the final period it is a single obstacle problem, which we solve, together with the regularity of its free boundary, by established methods. Before that period a partial hodograph transformation straightens both free boundaries and turns the problem into a quasilinear parabolic equation with oblique boundary conditions on a fixed interval. Comparison principles, explicit barriers and regularity theory for quasilinear equations then give existence, uniqueness and smoothness. Transforming back and gluing the two constructions yields global regularity: both free boundaries are infinitely differentiable and the value function is a classical solution at every positive wealth level. A dual budget process verifies optimality. We also derive coupled Volterra integral equations for the free boundaries, prove exponential convergence to the perpetual problem under a scalar condition, and find numerically a purchase threshold that is U-shaped in the time to retirement.

math.OC↗

arXiv2026

Renting, Owning, and Moving: Housing Tenure Choice with Transaction Costs

The wealth thresholds at which a household switches between renting and owning depend on its preferences, but the dates at which some owner sells or every renter buys do not. In our finite-horizon model, a household chooses consumption, a portfolio, and costly tenure changes while rents, ownership expenses, and transaction costs vary over time on announced dates. When financial markets span house-price risk, these dates are those of a deterministic minimum cost schedule for housing, discounted at the risk-adjusted housing carry and computed from a scalar reflected equation. Preferences, housing services, and labor income only locate the thresholds inside these timing windows, and house-price coefficients enter the dates only through the carry, because financial hedging offsets the exposure of the home. When owning costs at least as much as renting, the windows concern selling, and an anticipated selling surcharge closes the selling window before the surcharge peaks and keeps it closed for years afterwards. We also establish strong duality and the regularity of the thresholds and compute them by integral equations. Numerically, the windows disappear when short sales or borrowing are restricted but do not move with the preferences we vary under an uninsurable increase in the ownership cost.

math.OC↗

arXiv2026

Consumption and Investment with Multiple Job-Switching Opportunities

We study finite-horizon optimal switching with affine rewards in a consumption-investment model with finitely many occupational regimes. Directed shortest-path costs yield the exact natural borrowing limit. A dual transformation reduces the control problem to a one-dimensional system of variational inequalities with interconnected obstacles. Convexity and a distributional waiting inequality give local spatial $C^{1,1}$ regularity and smooth fit, including destination ties. These estimates establish strong duality and recover optimal consumption, investment, and switching strategies. A reflected backward stochastic differential equation representation yields a set-based integral formula without prescribed boundary geometry. Every connected component of the spatially regular locus is a maximal smooth graph over time. Exact examples exhibit disconnected contact sets, temporal boundaries under strict triangle costs, and a corner in an individual boundary component under additive route costs. A convergent time discretisation completes the analysis.

math.OC↗

arXiv2026

Sharp asymptotics for a free boundary touching a degenerate boundary: the perpetual Heston put

We study the exercise boundary of the perpetual American put in the Heston model near zero variance. There the pricing operator degenerates, and the exercise boundary, a free boundary in the stock--variance half-plane, touches the boundary of the half-plane. No Feller condition is imposed. The boundary is analytic at positive variance and extends as a regular $C^1$ curve tangent to the zero-variance axis. Its approach to the axis follows one of three laws, according to whether the Feller ratio $2κθ/σ^2$ is larger than, equal to, or smaller than one: a logarithmic correction to linear order, an exponential correction in the square root of the logarithm, or a fractional power. In the first two cases the leading coefficients are explicit and the tangent is not Hölder continuous at the axis. In the third case the exponent is selected by a possibly nonsymmetric stable operator on the axis, and the amplitude is finite and positive.

math.AP↗

arXiv2026

Interior smoothness and zero-variance geometry for finite-maturity Heston American puts

We study finite-maturity American puts in the Heston model without the Feller condition. At positive variance, the exercise boundary is smooth and strictly decreasing in remaining maturity and variance. At zero variance, the endpoint is locally Lipschitz in remaining maturity, the boundary moves with bounded speed in maturity uniformly down to zero variance, and it extends continuously to the axis. Each boundary slice at positive maturity has a regular $C^1$ closure tangent to the zero-variance axis, its stock threshold has variance derivative tending to minus infinity, and both partial derivatives of the inverse boundary graph vanish along the slice. The continuation premium at the axis contact stock is of order variance, and as a consequence smooth fit fails in the variance direction at the axis. At expiry the whole boundary, including its axis edge, converges to the strike. We give quantitative boundary gap bounds, an exact limiting weighted boundary Hessian, and vertical identities retaining the maturity term. Exact boundary gap equivalents remain open.

q-fin.MF↗

arXiv2026

A Mean Field Model of Consumption Inertia and Keeping Up with the Joneses

Households compare their living standard with others' and dislike changing it. We study consumption and investment when felicity depends on consumption relative to a benchmark, the population's geometric average consumption, and cuts in felicity weigh more than increases. Asset returns are exogenous. For finitely many types and arbitrary initial wealth and inherited standards, a mean field equilibrium exists under a weak interaction condition, and for fixed budget multipliers the benchmark is the fixed point of a contraction. In a complete market with common risk, a mean field equilibrium at empirical type frequencies is an exact Nash equilibrium of the finite game, for any preferences over relative consumption. We bound the gain from deviating when plans computed at another composition are used. We compute equilibria in which groups with different wealth, inherited standards, and loss aversion revise spending at different dates. With identical households and common risk, the unique symmetric equilibrium is the policy of a single loss averse household with modified curvature. In a baseline example, ignoring the inherited standard costs up to 17% of wealth, while small errors about the composition of the reference group cost less than 0.5%.

q-fin.PM↗

arXiv2026

Consumption adjustment with mean-reverting risk premia: A singular stochastic control approach

We study a two-sided singular stochastic control problem in which changes in consumption carry utility costs and the risk premium follows the mean-reverting Kim-Omberg model. Optimal consumption is reflected between two moving barriers given by thresholds that depend on the current risk premium. These thresholds are the stopping boundaries of a Dynkin game for a two-dimensional diffusion driven by a single Brownian motion. A sharp occupation estimate shows that they are Lipschitz in logarithmic scale, uniformly in the cost of reducing consumption, and that smooth fit holds along the diffusion direction at every contact point. Outside a bounded interval of risk premia and at most two further points, the thresholds are infinitely differentiable. As the reduction cost grows, optimal consumption converges to the ratcheting policy.

math.OC↗

arXiv2026

Consumption and Investment When Welfare Floors Change over Time

We study consumption and investment over a finite horizon when continuation utility must stay above a welfare floor that changes over time, and the floor at the horizon acts as a terminal wealth floor. A cumulative multiplier reduces the problem to a parabolic obstacle problem. When relative risk aversion exceeds one, the intervention boundary exists at every interior date. When it is below one, the boundary exists exactly at the dates where a discounted transformation of the floor is locally increasing and sets a strict running record, so it can disappear and later reenter. We prove local regularity of the boundary, construct the dual value from the obstacle solution, and verify the optimal cumulative multiplier, whose moments are controlled through its representation as a running supremum. Strong duality identifies the exact lower endpoint of feasible wealth. With stochastic income in a complete market, the floor becomes the value of an outside option, which links the boundary to limited commitment and endogenous borrowing capacity.

math.OC↗

arXiv2026

The Obstacle Problem Arising from the American Chooser Option

We study the finite-horizon obstacle problem associated with the American chooser option. Its obstacle is the maximum of two independently determined American call and put values and has a spatial kink where these values cross. Using truncation, penalization, and comparison, we construct a local strong Sobolev solution and prove uniqueness within an exponential-growth class. We show that contact occurs only on the smooth exercise-payoff branches and that both contact regions have nonempty sections at every time. We then establish strict monotonicity, terminal limits, and local Lipschitz continuity of the two free boundaries. Localized one-phase equations, quantitative nondegeneracy, and parabolic boundary Harnack estimates yield $C^\infty$ regularity on the open time interval.

math.AP↗

arXiv2026

Finite-Horizon Reversible Investment under Multi-Factor Dynamics

We study a finite-horizon reversible investment problem in which a risk-neutral firm adjusts capacity at a proportional purchase cost and a lower salvage value under multi-factor geometric Brownian motion. Via the singular control--optimal switching correspondence, the marginal value of capacity solves a family of parabolic double-obstacle problems. We prove existence, uniqueness and local Sobolev regularity of the strong solution, characterize investment, waiting and disinvestment regions by continuous, strictly separated free boundaries, and verify optimality of the reflected capacity process. Numerically, joint demand improvements shift both boundaries super-additively, 1.5--2.7 times as strongly at the disinvestment boundary, depending on factor correlation.

q-fin.MF↗

arXiv2026

Finite-Horizon Portfolio Choice, Labor Supply, and Early Retirement under Borrowing Constraints

We study a finite-horizon optimal consumption and portfolio problem with labor supply flexibility and an irreversible early retirement option under a borrowing constraint. The agent chooses consumption, risky investment, and leisure before retirement, while after retirement labor income disappears and leisure is fixed at its maximal level. Preferences are described by a Cobb--Douglas utility, and wealth must remain nonnegative. {Using a dual martingale method, we transform the primal problem into a zero-sum stopper--singular-controller game. The associated dual value is characterized by a min--max parabolic variational inequality with obstacle and gradient constraints. We show that the maximal strong solution of the resulting variational inequality is the unique admissible strong solution whose gradient-constrained free boundary, namely the binding boundary, is monotone increasing in calendar time. A verification argument then identifies this strong solution with the value of the stopper--singular-controller game, and duality recovers the optimal retirement, consumption, leisure, and portfolio policies.} The numerical analysis recovers the value function and optimal policies, and illustrates how labor supply flexibility affects consumption, portfolio choice, and retirement timing under borrowing constraints.

math.OC↗

arXiv2026

Finite-Horizon Optimal Consumption and Investment with Time-Varying Job-Switching Costs

In this paper, we study the finite-horizon problem of an economic agent's optimal consumption, investment, and job-switching decisions. The key new feature of our model is that the job-switching cost is time-varying. This extension leads to a novel mathematical characterization: the agent's dual problem reduces to a parabolic double obstacle problem with time-dependent upper and lower obstacles. By employing rigorous PDE theory, we establish not only the existence and uniqueness of the solution to this double obstacle problem, but also the smoothness of the two free boundaries that emerge from it. Building on these results, we characterize the agent's optimal consumption, portfolio, and job-switching strategies.

math.OC↗

arXiv2023

A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization

In this paper, we undertake an investigation into the utility maximization problem faced by an economic agent who possesses the option to switch jobs, within a scenario featuring the presence of a mandatory retirement date. The agent needs to consider not only optimal consumption and investment but also the decision regarding optimal job-switching. Therefore, the utility maximization encompasses features of both optimal switching and stochastic control within a finite horizon. To address this challenge, we employ a dual-martingale approach to derive the dual problem defined as a finite-horizon pure optimal switching problem. By applying a theory of the double obstacle problem with non-standard arguments, we examine the analytical properties of the system of parabolic variational inequalities arising from the optimal switching problem, including those of its two free boundaries. Based on these analytical properties, we establish a duality theorem and characterize the optimal job-switching strategy in terms of time-varying wealth boundaries. Furthermore, we derive integral equation representations satisfied by the optimal strategies and provide numerical results based on these representations.

math.OC↗

arXiv2021

A Unified Approach to Retirement and Consumption-Portfolio Choice

In this study we propose a unified model of optimal retirement, consumption and portfolio choice of an individual agent, which encompasses a large class of the models in the literature and provide a general methodology to solve the model. Different from the traditional approach, we consider the problems before and after retirement simultaneously and identify the difference in the dual value functions as the utility value of lifetime labor. The utility value has an option nature, namely, it is the maximized value of choosing the retirement time optimally and we discover it by solving a variational inequality. Then, we discover the dual value functions by using the utility value. We discover the value function and optimal policies by establishing a duality between the value function and the dual value function.

math.OC↗

arXiv2021

A problem of optimal switching and singular control with discretionary stopping in portfolio selection

In this paper we study the optimization problem of an economic agent who chooses a job and the time of retirement as well as consumption and portfolio of assets. The agent is constrained in the ability to borrow against future income. We transform the problem into a dual two-person zero-sum game, which involves a controller, who is a minimizer and chooses a non-increasing process, and a stopper, who is a maximizer and chooses a stopping time. We derive the Hamilton-Jacobi- Bellman quasi-variational inequality(HJBQV) of a max-min type arising from the game. We provide a solution to the HJBQV and verification that it is the value of the game. We establish a duality result which allows to derive the optimal strategies and value function of the primal problem from those of the dual problem.

math.OC↗

arXiv2019

Optimal Insurance with Limited Commitment in a Finite Horizon

We study a finite horizon optimal contracting problem of a risk-neutral principal and a risk-averse agent who receives a stochastic income stream when the agent is unable to make commitments. The problem involves an infinite number of constraints at each time and each state of the world. Miao and Zhang (2015) have developed a dual approach to the problem by considering a Lagrangian and derived a Hamilton-Jacobi-Bellman equation in an infinite horizon. We consider a similar Lagrangian in a finite horizon, but transform the dual problem into an infinite series of optimal stopping problems. For each optimal stopping problem we provide an analytic solution by providing an integral equation representation for the free boundary. We provide a verification theorem that the value function of the original principal's problem is the Legender-Fenchel transform of the integral of the value functions of the optimal stopping problems. We also provide some numerical simulation results of optimal contracting strategies

econ.TH↗

arXiv2018

Duesenberry's Theory of Consumption: Habit, Learning, and Ratcheting

This paper investigates the consumption and risk taking decision of an economic agent with partial irreversibility of consumption decision by formalizing the theory proposed by Duesenberry (1949). The optimal policies exhibit a type of the (s, S) policy: there are two wealth thresholds within which consumption stays constant. Consumption increases or decreases at the thresholds and after the adjustment new thresholds are set. The share of risky investment in the agent's total investment is inversely U-shaped within the (s, S) band, which generates time-varying risk aversion that can fluctuate widely over time. This property can explain puzzles and questions on asset pricing and households' portfolio choices, e.g., why aggregate consumption is so smooth whereas the high equity premium is high and the equity return has high volatility, why the risky share is so low whereas the estimated risk aversion by the micro-level data is small, and whether and when an increase in wealth has an impact on the risky share. Also, the partial irreversibility model can explain both the excess sensitivity and the excess smoothness of consumption.

econ.TH↗