• Dr. Rajni

Imagine the stock market as a landscape where each point represents a different combination of stocks. This landscape changes over time as stock prices fluctuate. Market diversity tells us how spread out the investments are in the market. If everyone invests in a few popular stocks, the market is less diverse. A more diverse market means that investments are spread across many different stocks. Market volatility refers to how much stock prices change over time. A volatile market is one where prices move up and down frequently. This paper provides a mathematical framework for creating investment strategies based on these two concepts: One key idea is to create a portfolio that benefits from market volatility while minimizing the impact of changes in market diversity. This is achieved using an exponentially concave function to guide investment allocation. A new measure of market volatility, called the L(α)-divergence, is introduced. This measure is more flexible than traditional methods and enables a broader range of investment strategies. Using these tools, the paper constructs portfolios that outperform the market, even when transaction costs are considered. This research provides a sophisticated approach to portfolio construction, allowing investors to develop strategies that are robust to market fluctuations and have the potential for higher returns.

Market diversity, Market volatility, Multiplicatively Generated Portfolio, L(α)-Divergence, Generalized Functional Portfolio Generation

"Application of Information Geometry in Stochastic Portfolio Theory", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.275-281, January-2019, Available :http://www.jetir.org/papers/JETIR1901J40.pdf

"Application of Information Geometry in Stochastic Portfolio Theory", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp275-281, January-2019, Available at : http://www.jetir.org/papers/JETIR1901J40.pdf