Author

Akihiro Tanaka

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Preprint Nov 2026

The Cost of Minimal Completeness: Gamma-to-Delta Aliasing in Discrete Markets

A $(d+1)$-state lattice is the smallest complete one-step approximation of a $d$-dimensional Brownian market. Its centered quadratic increments must lie in the span of the traded innovations. We study the resulting Gamma-to-Delta aliasing through the linear operator $\mathcal{A}_\xi(H)=\mathbb{E}[(\xi^\top H\xi-\operat...

Akihiro Tanaka · 1 citation

Preprint Oct 2026

Third-moment cancellation and predictable representation in finite-state BSDE approximation

We study finite-state approximations of Brownian-driven Markovian backward stochastic differential equations when the same one-step increment is used both for weak propagation and for martingale representation. For a centered isotropic state-independent increment with vanishing third moment, we prove first-order conver...

Akihiro Tanaka · 1 citation

Preprint Oct 2026

Initialization-Dependent Solution Selection by the Euler-Maruyama Scheme for a Degenerate SDE

We study the Euler-Maruyama approximation of the degenerate stochastic differential equation $dX_t = |X_t|^\alpha\,dW_t$, $0<\alpha<1/2$, $X_0 = 0$, for which uniqueness in law fails. The Euler scheme started exactly from zero is trapped by the absorbing solution, whereas a nonzero initialization $x_h \to 0$ can select...

Akihiro Tanaka · 0 citations