Jan Obłój, like many leading financial mathematicians, focuses his research on, among other things, modelling derivatives such as options and futures, using advanced probability theories. His work has become the foundation of financial strategies used by the world's largest institutions, combining the theoretical and practical aspects of risk and investment management. Let's take a look at Polak's most interesting findings.
Table of contents:
- Who is Jan Obłój?
- When to walk away from a casino table?
- Maximising profits while minimising losses: Investing with drawdown constraints
- How much is information worth in the market?
- Summary
Who is Jan Obłój?
Jan Obłój is an eminent financial mathematician, specialising in probability theory, derivatives pricing and financial modelling. He is a professor at the University of Oxford, where he conducts research and teaches.
Obłój has gained recognition for his contributions to the development of Skorokhod embedding theory, option pricing and hedging strategies. His work is widely cited and used in financial practice around the world.
He has collaborated with many well-known mathematicians and financiers, and his research is applicable to both the theory and practice of financial markets. He is an active member of the academic community, publishing in prestigious journals and attending conferences. He was awarded a professorship at Oxford University and the Hugo Steinhaus Main Prize of the Polish Mathematical Society. His work has been cited in over 1000 peer-reviewed titles.
When to walk away from a casino table?
Jan Obłój has devoted several of his works to the subject of gambling, focusing on the question: ‘When to stop gambling?’. His research is directly applicable to the investment world, particularly in the context of active trading.
In the article ‘Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model’ examined the impact of the exit strategy dependent on the history of the plant (so-called path-dependent). For example, if a player has lost several bets in a row, he may choose to exit the game to avoid further losses, even though he has not yet lost much at any given time. Alternatively, it may add an element of randomness to the decision to continue playing. For example, a player might decide to flip a coin after each losing round to decide whether to continue playing. If an eagle falls out, he continues the game, and if a headsign, he ends the game.
The study found that betting history-dependent strategies and the addition of randomness to decisions can improve player performance compared to path-independent strategies, where end-of-game decisions are made solely on the basis of current profit or loss. Adding random decisions, such as a coin flip, can help players perform better, avoiding large losses and maximising profits.
Another study on exit strategies was the article ‘Optimal Exit Time from Casino Gambling: Strategies of Precommitted and Naïve Gamblers’, which analysed two types of gamblers: committed gamblers, who stick to a predetermined strategy, and naïve gamblers, who may change their strategy during the course of the game. It found that declared gamblers tend to avoid large losses by using loss-exit strategies, while naive gamblers can continue playing despite increasing losses. Strategies that depend on betting history and randomisation can lead to better results, helping players to manage risk much better.
Maximising profits while minimising losses: Investing with drawdown constraints
In the article ‘The Numéraire Property and Long-Term Growth Optimality for Drawdown-Constrained Investments’, the authors, including Jan Obłój, discuss how investors can maximise their returns over the long term while minimising the risk of large losses.
The strategy is to set a maximum allowable drawdown from a portfolio's maximum value (known as a drawdown). For example, if one sets a drawdown of 10 per cent, this means that the portfolio value should not fall below 90 per cent of its maximum value.
Investors should then choose safe assets, such as government bonds, which have low risk and are stable, and risky assets, such as equities or cryptocurrencies, which have potentially higher returns but also higher risk. However, the strategy requires regular monitoring and periodic adjustment of the portfolio composition to ensure that it meets the drawdown limits set.
For example, if we set a maximum drawdown of 10 per cent, the initial portfolio composition could be 60 per cent technology stocks and 40 per cent government bonds. We regularly check the value of the portfolio. If its value falls by 8 per cent, we increase the share of bonds to 50 per cent to reduce the risk of further losses. Introducing drawdown constraints helps investors to avoid significant declines in the value of the portfolio, while maintaining its growth potential.
The article highlights that optimal investment strategies can be achieved through dynamic portfolio adjustment, which is crucial for long-term financial success.
How much is information worth in the market?
In the article ‘Robust Framework for Quantifying the Value of Information in Pricing and Hedging’, Jan Obłój examines how differences in access to information affect the pricing and hedging of financial instruments. He compares two individuals: one who only observes share prices in the market, and another who has additional information that can help to better predict future prices.
The authors present a model to value how much access to additional information is worth. To do this, they use the concept of so-called superhedging, or hedging strategies that protect against worst-case scenarios. An agent with additional information can limit its strategies to certain price paths, which gives it an advantage. The authors show that such an advantage can be expressed in the form of simpler mathematical models. The article highlights how the value of such information can be mathematically calculated and how it affects investment strategies.
Summary
In conclusion, Jan Obloj's work provides valuable guidance on risk and investment management, both in a theoretical and practical context. Adding the effect of randomness to our investment strategies, or basing an exit strategy on recent trades, seems more effective than assuming a predetermined outcome or a borderline loss. The second aspect is to stick to the strategy one has established while playing. This also seems more effective than trying to modify it over time.
Grzegorz Dróżdż, CAI MPW, Market Analyst of Conotoxia Ltd. (Conotoxia investment service)
The above trade publication does not constitute an investment recommendation or information recommending or suggesting an investment strategy within the meaning of Regulation (EU) No. 596/2014 of April 16, 2014. It has been prepared for informational purposes and should not form the basis for investment decisions. Neither the author of the publication nor Conotoxia Ltd. shall be liable for investment decisions made on the basis of the information contained herein. Copying or reproducing this publication without written permission from Conotoxia Ltd. is prohibited. Past performance is not a reliable indicator of future results.
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