10 problems

Let $b^{\star}$ denote the optimal extraction boundary, and let $\lambda_{\mathpzc{p}}>0$ be the positive-jump intensity parameter. Monotonicity conjecture. The mapping … is increa…

Consider the time-homogeneous jump-diffusion stochastic differential equation … where $\xi\in\mathbb{R}$, $\mu,\sigma,\rho\colon\mathbb{R}\to\mathbb{R}$ are measurable,…

Let $(\bar V_s)_{s\in[0,t]}$ be the innovation process, let $Y_0$ be the initial observation, and let … be the family of observed jump counts. Assume that Assumption SDE holds and…

Innovation-process information conjecture. The sigma-algebra generated by $(\bar V_s)_{s\in[0,t]}$ and $Y_0$ should coincide with the sigma-algebra generated by $(Y_s)_{s\in[0,t]}$…

Discontinuous-viscosity-solution conjecture. The function $V$ is only a discontinuous viscosity solution of

Conjecture on local asymptotic normality and efficiency. Under these conditions, the jump-diffusion model is locally asymptotically normal with rate $\sqrt{n\Delta_n}$ for the drif…

Consider a jump-diffusion model observed at times with mesh $[?$. Let $\theta=(\theta_1,\theta_2)$ consist of drift and jump components and diffusion components, respectively, and…

Extended nonequidistant rate conjecture. The same equality should hold when $b\not\equiv 0$ and $c\not\equiv 0$:

Exact-rate conjecture. The exact rate of convergence of the minimal errors in $\chi^{\rm noneq}$ is the same as for $\chi^{\rm noneq*}$.

Consider a Markovian claim $X=X^y$ driven by a jump diffusion $Y$, with drift $b$, volatility $sigma$, jump coefficients $gamma^{(i)}$, compensator measures $nu^i$, running loss…