15 problems

Consider the extremal investor model with $x_0=0$, parameter $\alpha=1$, and Gaussian innovations of standard deviation $1$. Define … Thus $w_n$ is the greatest distance between…

The FHD equation is considered in the Black–Scholes framework, and the reconstructions in Figure 3 are reconstructions of local-volatility surfaces from option-price data. Multisol…

In the single-factor model, let the market variance be $\sigma_M^2$, let the idiosyncratic variances be $\sigma_i^2$, let the nonnegative beta factors be $\beta_i$, and let…

Let $t\in [t_n,t_{n+1})$. For fixed $n$ and $k\leq n$, define the filtrations … where $\overline{H}_n:= (H_1,\ldots,H_n)$, $\mathbb{F}^B$ is the Brownian filtration,…

Let $s^+(t)$ and $s^-(t)$ denote the upper and lower boundaries of the spread, let $\u03bb$ be the parameter appearing in the Stefan problem, let $b1$ be the drift parameter, and l…

In the stochastic-liquidity Kyle model, let the fundamental price $\tilde v$ be normally distributed, let the informed trader's trading rate denote the rate at which that trader tr…

First-order approximation conjecture. First-order approximation of equilibrium decision-rules based on the notion of materiality yields decision-rules using functions of the form

All-time positivity conjecture. For every feedback gain satisfying

The model describes a macroscopic portfolio system derived from microscopic agent dynamics, with traders exhibiting chartist or fundamental behavior and with prices generated by th…

For each asset-price time series, form its trajectory matrix by the maximal trajectory-matrix construction used in the source, and consider the matrix's spectral distribution and s…

Let the log-return distributions of large-cap equities be viewed as probability distributions, with scale and location allowed to vary. First Universality Conjecture. The distribut…

Ayed–Kuo insider-trading solution conjecture. The solution is

Let $g^+$ and $g^-$ denote the positive and negative density functions in the space-homogeneous deterministic mean field Cross model. The steady states are classified into types…

Let market depth denote the sensitivity of prices to the total order, so that its reciprocal is the price impact of the total order. Kyle's conjecture. Neither increasing nor decre…

Maximum-drawdown distribution conjecture. The distribution of maximum drawdown is related both to the distribution of the supremum of reflected fractional Brownian motion and to th…