Portfolio Choice with Competing Precautionary and Accumulation Goals

Battle Count: 74

The paper is primarily focused on household finance and goal-based portfolio management rather than institutional quantitative trading. However, it has indirect relevance: (1) the HJB/viscosity solution methodology is standard in quantitative finance, (2) the Sharpe ratio and market parameters are calibrated to equity market data, (3) the optimal portfolio allocation results could inform systematic robo-advisory strategies, (4) the deadline pressure and crowding-out effects are relevant for any portfolio with competing time-horizon objectives. The paper is more applicable to wealth management and robo-advisory than to high-frequency or algorithmic trading.

Implementation requires: (1) solving two single-goal HJB PDEs numerically (one parabolic, one elliptic), (2) constructing continuation and terminal operators via numerical integration over goal distributions, (3) solving the dual-goal HJB backward in time with implicit Euler and upwind differencing, (4) handling non-monotonic value functions and threshold-crossing policies, (5) implementing Howard policy iteration for the stationary random-deadline problem, (6) performing quadrature over lognormal/truncated distributions. The viscosity solution theory and proof verification add significant mathematical complexity. The binomial benchmark is simpler but the full continuous-time model requires careful numerical treatment near non-smooth regions.

The paper provides detailed calibration parameters (λ from BLS JOLTS data, goal amounts from College Board and JP Morgan, market parameters from Lettau-Ludvigson), a complete numerical algorithm (implicit Euler, upwind differencing, Thomas algorithm, Howard policy iteration), and extensive sensitivity analysis. However, no code repository is provided. The mathematical proofs are complete and self-contained. All parameter ranges and baseline values are explicitly stated.