arXiv subjects

Philip Maymin

Publications and source records attributed to Philip Maymin.

8 recordsLinked to original sources

arXiv2026

Dynamic Tracking Error and the Total Portfolio Approach

Strategic Asset Allocation and the Total Portfolio Approach differ in one thing: the tracking error the board grants the chief investment officer. The board's first decision should be the drawdown it can tolerate; the benchmark and tracking error budget follow. The value comes from spending that budget dynamically, adding active risk when the reward is high and shedding it as the fund nears its limit. Managed this way, a fund would have compounded about two percentage points a year faster at the same drawdown, with no security selection. What matters is dynamic versus static tracking error, not the label.

q-fin.PM↗

arXiv2010

Markets are efficient if and only if P = NP

I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.

q-fin.GN↗

arXiv2010

The Minimal Model of Financial Complexity

A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy. This simple, unique, and robust model is the smallest possible deterministic model of financial complexity, and its generalization leads to complex variety. Compared to a random walk, the minimal model generates time series with fatter tails and more frequent crashes, thus more closely matching the real world. It does all this without any parameter fitting.

q-fin.TR↗

arXiv2010

Regulation Simulation

A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate the effects of financial regulation that either pricks bubbles, props up crashes, or both. The results suggest that regulation makes the market process appear more Gaussian and less complex, with the difference more pronounced for more frequent intervention, though particular periods can be worse than the non-regulated version, and that pricking bubbles and propping up crashes are not symmetrical.

q-fin.GN↗

arXiv2010

The Hazards of Propping Up: Bubbles and Chaos

In the current environment of financial distress, many governments are likely to soon become major holders of financial assets, but the policy debate focuses only on the likelihood and extent of short-term market stabilization. This paper shows that government intervention and propping up are likely to lead to long-term bubbles and even wildly chaotic behavior. The discontinuities occur when the committed capital reaches a critical amount that depends on just two parameters: the market impact of trading and the target exposure percentage.

q-fin.GN↗

arXiv1997

Programming Complex Systems

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilities can be negative, and events can cancel out. An illustration of the power of quantumized algorithms is the ability to efficiently solve the satisfiability problem, something that many believe is beyond the capability of classical computers. This paper proves that the lambda-q calculus is not only capable of solving satisfiability but can also simulate such complex systems as quantum computers. Since satisfiability is believed to be beyond the capabilities of quantum computers, the lambda-q calculus may be strictly stronger.

quant-ph↗

arXiv1997

The lambda-q calculus can efficiently simulate quantum computers

We show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines. We conclude by noting that the lambda-q calculus may be strictly stronger than quantum computers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but there is a widespread doubt that they are efficiently solvable by quantum computers.

quant-ph↗

arXiv1997

Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms

This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification of classical programming languages. As an intermediary step, we introduce a formal metalanguage called the lambda-p calculus for the specification of programming languages that allow true random number generation. We demonstrate how selected randomized algorithms can be programmed directly in the lambda-p calculus. We also demonstrate how satisfiability can be solved in the lambda-q calculus.

quant-ph↗