TCS Research & Innovation
Portfolio Optimization is a fundamental process in financial planning which involves constant redistribution of the investment into various financial products with an primary objective of maximal profits with minimal risks. In mathematical terms, it’s a process involving continuous analysis of financial asset’s data to make optimal sequential decisions i.e a classical prospective problem for reinforcement learning and deep learning. As financial markets evolves continuously over time without constant dynamics and the information regarding the financial products is diverse in many aspects, a robust and adaptive financial system with generic implementation to different financial markets such as stocks, forex and cryptos is essential.
In this project, all the frameworks has a fundamental aim of maximising forecasted profits and also minimising calculated risks through optimal asset allocation for a given fixed time horizon. For experimental purposes, any financial market is constructed using relavant asset information with an assumption that it has sufficient liquidity so that any order gets transacted with negligible market impact. This market system with operational dynamics is casted into a simulated environment for all purposes. For portfolio allocation, we consider adaptive autonomous agent that gathers all required information from market to make decisions and to improve its trading strategy through several interacting experiences.
Let’s consider the number of financial assets that agent would invest is \( N \). For simplicity, we assume our total investment capital is 1.0 unit base asset at initial timeperiod. Now, let’s define relative price vector of close-open prices and portfolio weight vector where \( \frac{v_{i, t}^{close}}{v_{i, t}^{open}} \) is relative price and \( w_{i,t} \) is the fraction of capital of asset \(i\) at timeperiod \(t\).
\[y_t=[1, \frac{v_{1,t}^{close}}{v_{1,t}^{open}}, \frac{v_{2,t}^{close}}{v_{2,t}^{open}},\cdots,\frac{v_{N,t}^{close}}{v_{N,t}^{open}}]\] \[w_t=[w_{0,t}, w_{1, t}, \cdots, w_{N, t}]\] \[\sum_{i=0}^{N}w_{i, t}=1\]In any fixed horizon simulation, the total capital value after timestamp \(T\) while considering the transaction cost factor \( \mu \) is
\[p_T=\prod_{t=1}^{T}(1-\mu\sum{|\frac{y_t \odot w_{t-1}}{y_t \cdot w_{t-1}} - w_{t}|}) y_t\cdot w_{t-1}\]The trading agent with desired objective is achieved through different formulations such as
Reinforcement learning formulation: The interaction between the simulated environment and the trading agent can be formulated into Markov Decision Process with appropriate state, action and reward mechanisms. This MDP formulation can be solved using various model-free reinforcement algorithms such as DQN, DDPG, PPO, SAC etc…
Deep learning formulation: Using the appropriate assumptions, this problem can be formulated into supervised learning framework, where state-action-reward can be viewed as input-output-objective. This is typically one-way to model this problem and there exists several ways in which this problem can be solved using deep learning.
Note: There is only limited amount of information and no project-code here due to TCS confidentiality and Intellectual property rights
To conclude, there is alot of scope for advancements using machine learning and reinforcement learning in the problem of wealth management in the domain of Quantitative finance.