We consider a large trader seeking to liquidate a portfolio using both a transparent trading venue and a dark pool. Our model captures the price impact of trading in transparent traditional venues as well as the execution uncertainty of trading in a dark pool. The unique optimal execution strategy uses both venues continuously. The order size in the dark pool can overor underrepresent the portf...

In this paper, Black Scholes’s pricing model was developed to study American option on future contracts of Brent oil. The practical tests of the model show that market priced option contracts as future contracts less than what model did, which mostly represent option contracts with price rather than without price. Moreover, it suggests call option rather than put option. Using t hypothesis test...

We use a mean-variance model to analyze the problem of decentralized portfolio management. We find the solution for the optimal portfolio allocation for a head trader operating in n different markets, which is called the optimal centralized portfolio. However, as there are many traders specialized in different markets, the solution to the problem of optimal decentralized allocation should be di...

Pairs trading is an investment strategy that exploits the short-term price difference (spread) between two co-moving stocks. Recently, pairs methods based on deep reinforcement learning have yielded promising results. These can be classified into approaches: (1) indirectly determining actions and stop-loss boundaries (2) directly spread. In former approach, boundary completely dependent boundar...

4. Each trader also has a utility function ui : R+ → R+ and wants to maximize his own utility; Suppose each good j has a price pj ≥ 0. Without loss of generality, we assume the price vector p = (p1, p2, . . . , pn) satisfies ∑n j=1 pj = 1. We give the definition of optimal bundles: Definition 2 (Optimal Bundle). Given p ∈ ∆n and bi = ei · p = ∑ j∈[n] eij · pj, then xi ∈ R+ is an optimal bundle ...

We compare optimal static and dynamic solutions in trade execution. An execution problem is considered where a trader looking at short-term price predictive signal while trading. When the creates an instantaneous market impact, it shown that transaction costs of adaptive strategies are substantially lower than corresponding strategy. In same spirit, case transient observe finite number times ca...

Market traders trade gold, and Bitcoin is aim to maximize their return. This paper utilizes the grey prediction model explore optimal trading strategy optimize fund allocation based on dynamic programming. In addition, by comparing with other traditional strategies, we discover that can more accurately estimate future prices, enabling trader gain steadily growing returns at a low-risk level.

We develop a High Frequency (HF) trading strategy where the HF trader uses her superior speed to process information and to post limit sell and buy orders. We introduce a multi-factor self-exciting process which allows for feedback effects in market buy and sell orders and the shape of the limit order book (LOB). The model accounts for arrival of market orders that influence activity, trigger o...