In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift and fractional diffusion. Since the DO process is a semi-martingale, it can be represented as an \Ito diffusion. It turns out that in this framework the process for the spot price $S_t$ is a geometric BM with stochastic instantaneous volatility $\sigma_t$, the process for $\sigma_t$ is also a geometric BM with stochastic speed of mean reversion and time-dependent colatility of volatility, and the supplementary process $\calV_t$ is the Ornstein-Uhlenbeck process with time-dependent coefficients, and is also a function of the Hurst exponent. We also introduce an adjusted DO process which provides a uniformly good approximation of the fractional BM for all Hurst exponents $H \in [0,1]$ but requires a complex measure. Finally, the characteristic function (CF) of $\log S_t$ in our model can be found in closed form by using asymptotic expansion. Therefore, pricing options and variance swaps (by using a forward CF) can be done via FFT, which is much easier than in rough volatility models.

Disagreement is an essential element of science and life in general. The amount of disagreement is often quantified by highly abstract entropic measures such as the R\'enyi divergence. Despite their widespread use in science and engineering, such quantities lack numerical intuition and their axiomatic definitions contain no practical insight as to how the disagreement can be resolved. An economic approach addresses both of these problems by transforming disagreements into tangible investment opportunities. The R\'enyi divergence appears connected to the optimized performance of such investments. Optimization around individual opinions provides a social mechanism by which funds flow naturally to support a more accurate view. Such social mechanisms can help to resolve difficult disagreements (e.g., financial arguments concerning future climate).

Connected and automated vehicles (CAVs) are expected to yield significant improvements in safety, energy efficiency, and time utilization. However, their net effect on energy and environmental outcomes is unclear. Higher fuel economy reduces the energy required per mile of travel, but it also reduces the fuel cost of travel, incentivizing more travel and causing an energy "rebound effect." Moreover, CAVs are predicted to vastly reduce the time cost of travel, inducing further increases in travel and energy use. In this paper, we forecast the induced travel and rebound from CAVs using data on existing travel behavior. We develop a microeconomic model of vehicle miles traveled (VMT) choice under income and time constraints; then we use it to estimate elasticities of VMT demand with respect to fuel and time costs, with fuel cost data from the 2017 United States National Household Travel Survey (NHTS) and wage-derived predictions of travel time cost. Our central estimate of the combined price elasticity of VMT demand is -0.4, which differs substantially from previous estimates. We also find evidence that wealthier households have more elastic demand, and that households at all income levels are more sensitive to time costs than to fuel costs. We use our estimated elasticities to simulate VMT and energy use impacts of full, private CAV adoption under a range of possible changes to the fuel and time costs of travel. We forecast a 2-47% increase in travel demand for an average household. Our results indicate that backfire - i.e., a net rise in energy use - is a possibility, especially in higher income groups. This presents a stiff challenge to policy goals for reductions in not only energy use but also traffic congestion and local and global air pollution, as CAV use increases.

We present some indications of inefficiency of the Brazilian stock market based on the existence of strong long-time cross-correlations with foreign markets and indices. Our results show a strong dependence on foreign markets indices as the S\&P 500 and CAC 40, but not to the Shanghai SSE 180, indicating an intricate interdependence. We also show that the distribution of log-returns of the Brazilian BOVESPA index has a discrete fat tail in the time scale of a day, which is also a deviation of what is expected of an efficient equilibrated market. As a final argument of the inefficiency of the Brazilian stock market, we use a neural network approach to forecast the direction of movement of the value of the IBOVESPA future contracts, with an accuracy allowing financial returns over passive strategies.

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness, however, substantially diminishes when the portfolios concerned involve a high dimension of derivative positions with nonlinear payoffs; lack of closed form pricing solution for these potentially highly correlated, American-style derivatives further complicates the problem. This paper proposes a generic simulation-based algorithm for VaR estimation that can be easily applied to any existing procedures. Our proposal leverages cross-sectional information and applies variable selection techniques to simplify the existing simulation framework. Asymptotic properties of the new approach demonstrate faster convergence due to the additional model selection component introduced. We have also performed sets of numerical results that verify the effectiveness of our approach in comparison with some existing strategies.

The effect of proportional transaction costs on systematically generated portfolios is studied empirically. The performance of several portfolios (the index tracking portfolio, the equally-weighted portfolio, the entropy-weighted portfolio, and the diversity-weighted portfolio) in the presence of dividends and transaction costs is examined under different configurations involving the trading frequency, constituent list size, and renewing frequency. Moreover, a method to smooth transaction costs is proposed.

Inspired by Strotz's consistent planning strategy, we formulate the infinite horizon mean-variance stopping problem as a subgame perfect Nash equilibrium in order to determine time consistent strategies with no regret. Equilibria among stopping times or randomized stopping times may not exist. This motivates us to consider the notion of liquidation strategies, which lets the stopping right to be divisible. We then argue that the mean-standard deviation variant of this problem makes more sense for this type of strategies in terms of time consistency. It turns out that an equilibrium liquidation strategy always exists. We then analyze whether optimal equilibrium liquidation strategies exist and whether they are unique and observe that neither may hold.