We propose an algorithm which predicts each subsequent time step relative to the previous timestep of intractable short rate model (when adjusted for drift and overall distribution of previous percentile result) and show that the method achieves superior outcomes to the unbiased estimate both on the trained dataset and different validation data.

We propose a mathematical model of momentum risk-taking, which is essentially real-time risk management, focused on short-term volatility of stock markets. Its implementation, an automated momentum equity trading system, proved to be successful in extensive historical and real-time experiments, discussed in the paper. Risk-taking is one of the key components of general decision-making, a challenge for artificial intelligence and machine learning. We begin with a relatively simple new algebraic-type theory of news impact on share-prices, which describes well their power growth, periodicity, logarithmic periodicity, and the market phenomena like price targets and profit-taking; Bessel and hypergeometric functions are used. Its discretization results in some tables of bids, expected returns for different investment horizons. This is a new approach; its preimage is a new contract card game presented at the end, a combination of bridge and poker. The relations to random processes and fractional Brownian motion are outlined. We provide a reasonably complete description of our AI-type trading system, but our ML procedures are not discussed much (a special version of those in neural networking is used).

A counterparty credit limit (CCL) is a limit imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. Although CCLs are designed to help institutions mitigate counterparty risk by selective diversification of their exposures, their implementation restricts the liquidity that institutions can access in an otherwise centralized pool. We address the question of how this mechanism impacts trade prices and volatility, both empirically and via a new model of trading with CCLs. We find empirically that CCLs cause little impact on trade. However, our model highlights that in extreme situations, CCLs could serve to destabilize prices and thereby influence systemic risk.

In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black--Scholes (BS) model. Our first result says that in the case where the game contingent claim (GCC) can be exercised only on a finite set of times, there exists an optimal strategy. Our second and main result is an example which demonstrates that for the case where the GCC can be stopped on the all time interval, optimal portfolio strategies need not always exist.

Traditional US rental housing data sources such as the American Community Survey and the American Housing Survey report on the transacted market - what existing renters pay each month. They do not explicitly tell us about the spot market - i.e., the asking rents that current homeseekers must pay to acquire housing - though they are routinely used as a proxy. This study compares governmental data to millions of contemporaneous rental listings and finds that asking rents diverge substantially from these most recent estimates. Conventional housing data understate current market conditions and affordability challenges, especially in cities with tight and expensive rental markets.

The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to derive the risk loadings. No matter which premium principle is used, some risk loading parameters should be given in advance subjectively. To overcome this subjective problem and calculate the risk premium more reasonably and objectively, we propose a top-down method to calculate these risk loading parameters. First, we implement the bootstrap method to calculate the total risk premium of the portfolio. Then, under the constraint that the portfolio's total risk premium should equal the sum of the risk premiums of each policy, the risk loading parameters are determined. During this process, besides using generalized linear models, three kinds of quantile regression models are also applied, namely, traditional quantile regression model, fully parametric quantile regression model, and quantile regression model with coefficient functions. The empirical result shows that the risk premiums calculated by the method proposed in this study can reasonably differentiate the heterogeneity of different risk classes.

In this paper, we analyze maximum Sharpe ratio when the number of assets in a portfolio is larger than its time span. One obstacle in this large dimensional setup is the singularity of the sample covariance matrix of the excess asset returns. To solve this issue, we benefit from a technique called nodewise regression, which was developed by Meinshausen and Buhlmann (2006). It provides a sparse/weakly sparse and consistent estimate of the precision matrix, using the Lasso method. We analyze three issues. One of the key results in our paper is that mean-variance efficiency for the portfolios in large dimensions is established. Then tied to that result, we also show that the maximum out-of-sample Sharpe ratio can be consistently estimated in this large portfolio of assets. Furthermore, we provide convergence rates and see that the number of assets slow down the convergence up to a logarithmic factor. Then, we provide consistency of maximum Sharpe Ratio when the portfolio weights add up to one, and also provide a new formula and an estimate for constrained maximum Sharpe ratio. Finally, we provide consistent estimates of the Sharpe ratios of global minimum variance portfolio and Markowitz's (1952) mean variance portfolio. In terms of assumptions, we allow for time series data. Simulation and out-of-sample forecasting exercise shows that our new method performs well compared to factor and shrinkage based techniques.

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A ore fundamental problem when extending the distorted expectation to a dynamic setting is {\it time-inconsistency}, that is, the usual "tower property" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.