Optimal capital allocation between different assets is an important financial problem, which is generally framed as the portfolio optimization problem. General models include the single-period and multi-period cases. The traditional Mean-Variance model introduced by Harry Markowitz has been the basis of many models used to solve the portfolio optimization problem. The overall goal is to achieve the highest return and lowest risk in portfolio optimization problems. In this paper, we will present an optimal portfolio based the Markowitz Mean-Variance-Skewness with weight constraints model for short-term investment opportunities in Iran's stock market. We will use a neural network based predictor to predict the stock returns and measure the risk of stocks based on the prediction errors in the neural network. We will perform a series of experiments on our portfolio optimization model with the real data from Iran's stock market indices including Bank, Insurance, Investment, Petroleum Products and Chemicals indices. Finally, 8 different portfolios with low, medium and high risks for different type of investors (risk-averse or risk taker) using genetic algorithm will be designed and analyzed.

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.

This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast electricity price spreads between different hours of the day. This supports an optimal day ahead storage and discharge schedule, and thereby facilitates a bidding strategy for a merchant arbitrage facility into the day-ahead auctions for wholesale electricity. The four latent moments of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the mean, variance, skewness and kurtosis of the densities to respond hourly to such factors as weather and demand forecasts. The best specification for each spread is selected based on the Pinball Loss function, following the closed form analytical solutions of the cumulative density functions. Those analytical properties also allow the calculation of risk associated with the spread arbitrages. From these spread densities, the optimal daily operation of a battery storage facility is determined.

This paper prices and replicates the financial derivative whose payoff at $T$ is the wealth that would have accrued to a $\$1$ deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black-Scholes market, Ordentlich and Cover (1998) only priced this derivative at time-0, giving $C_0=1+\sigma\sqrt{T/(2\pi)}$. Of course, the general time-$t$ price is not equal to $1+\sigma\sqrt{(T-t)/(2\pi)}$. I complete the Ordentlich-Cover (1998) analysis by deriving the price at any time $t$. By contrast, I also study the more natural case of the best levered rebalancing rule in hindsight. This yields $C(S,t)=\sqrt{T/t}\cdot\,\exp\{rt+\sigma^2b(S,t)^2\cdot t/2\}$, where $b(S,t)$ is the best rebalancing rule in hindsight over the observed history $[0,t]$. I show that the replicating strategy amounts to betting the fraction $b(S,t)$ of wealth on the stock over the interval $[t,t+dt].$ This fact holds for the general market with $n$ correlated stocks in geometric Brownian motion: we get $C(S,t)=(T/t)^{n/2}\exp(rt+b'\Sigma b\cdot t/2)$, where $\Sigma$ is the covariance of instantaneous returns per unit time. This result matches the $\mathcal{O}(T^{n/2})$ "cost of universality" derived by Cover in his "universal portfolio theory" (1986, 1991, 1996, 1998), which super-replicates the same derivative in discrete-time. The replicating strategy compounds its money at the same asymptotic rate as the best levered rebalancing rule in hindsight, thereby beating the market asymptotically. Naturally enough, we find that the American-style version of Cover's Derivative is never exercised early in equilibrium.

We give an explicit algorithm and source code for constructing risk models based on machine learning techniques. The resultant covariance matrices are not factor models. Based on empirical backtests, we compare the performance of these machine learning risk models to other constructions, including statistical risk models, risk models based on fundamental industry classifications, and also those utilizing multilevel clustering based industry classifications.

We demonstrate using multi-layered networks, the existence of an empirical linkage between the dynamics of the financial network constructed from the market indices and the macroeconomic networks constructed from macroeconomic variables such as trade, foreign direct investments, etc. for several countries across the globe. The temporal scales of the dynamics of the financial variables and the macroeconomic fundamentals are very different, which make the empirical linkage even more interesting and significant. Also, we find that there exist in the respective networks, core-periphery structures (determined through centrality measures) that are composed of the similar set of countries -- a result that may be related through the `gravity model' of the country-level macroeconomic networks. Thus, from a multi-lateral openness perspective, we elucidate that for individual countries, larger trade connectivity is positively associated with higher financial return correlations. Furthermore, we show that the Economic Complexity Index and the equity markets have a positive relationship among themselves, as is the case for Gross Domestic Product. The data science methodology using network theory, coupled with standard econometric techniques constitute a new approach to studying multi-level economic phenomena in a comprehensive manner.

Stock prices are influenced by numerous factors. We present a method to combine these factors and we validate the method by taking the international stock market as a case study. In today's increasingly international economy, return and volatility spillover effects across international equity markets are major macroeconomic drivers of stock dynamics. Thus, foreign market information is one of the most important factors in forecasting domestic stock prices. However, the cross-correlation between domestic and foreign markets is so complex that it would be extremely difficult to express it explicitly with a dynamical equation. In this study, we develop stock return prediction models that can jointly consider international markets, using multimodal deep learning. Our contributions are three-fold: (1) we visualize the transfer information between South Korea and US stock markets using scatter plots; (2) we incorporate the information into stock prediction using multimodal deep learning; (3) we conclusively show that both early and late fusion models achieve a significant performance boost in comparison with single modality models. Our study indicates that considering international stock markets jointly can improve prediction accuracy, and deep neural networks are very effective for such tasks.

We develop an optimal currency hedging strategy for fund managers who own foreign assets to choose the hedge tenors that maximize their FX carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is Cash Flow at Risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buckets to maximize (minimize) the expected FX carry benefit (cost), given the constraint that the CFaRs in all the future time buckets do not breach a predetermined liquidity budget. We demonstrate the methodology via an illustrative example where shorter-dated forwards are assumed to deliver higher carry trade returns (motivated by the historical experience where AUD is the domestic currency and USD is the foreign currency). We also introduce a tenor-ranking method which is useful when this assumption fails. We show by Monte Carlo simulation and by backtesting that our hedging strategy successfully operates within the liquidity budget. We provide practical insights on when and why fund managers should choose short-dated or long-dated tenors.

This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing rule will sell a precise amount of the outperforming stock and put the proceeds into the underperforming stock. Under typical conditions, in hindsight one can find pairs rebalancing rules that would have spectacularly beaten the market. Our trading strategy, which extends Ordentlich and Cover's (1998) "max-min universal portfolio," guarantees to achieve an acceptable percentage of the hindsight-optimized wealth, a percentage which tends to zero at a slow (polynomial) rate. This means that on a long enough investment horizon, the trader can enforce a compound-annual growth rate that is arbitrarily close to that of the best pairs rebalancing rule in hindsight. The strategy will "beat the market asymptotically" if there turns out to exist a pairs rebalancing rule that grows capital at a higher asymptotic rate than the market index. The advantages of our algorithm over the Ordentlich and Cover (1998) strategy are twofold. First, their strategy is impossible to compute in practice. Second, in considering the more modest benchmark (instead of the best all-stock rebalancing rule in hindsight), we reduce the "cost of universality" and achieve a higher learning rate.