OUR AUTHORS

His approach begins with that distinction and follows its consequences through conditional expectation, changes of probability measure, filtering equations and approximation methods. Exact cases provide a starting point: they show what a filter computes before a more general argument explains why the construction works. Density plots and contours give the reader a picture to examine; the assumptions and proofs establish what the picture can support.

He gives particular attention to the limits of an estimate. A narrow conditional distribution need not establish that the observation model is adequate, and an approximation should be judged against the quantity it is intended to recover. Algorithm descriptions therefore state their inputs, their mathematical target and the conditions on which their interpretation depends.

He writes for graduate students, researchers and mathematically trained practitioners who want a connected account of stochastic filtering, with the reasoning kept visible from the first conditioning operation to the final approximation.

She came to the question through reinsurance. Her first years after her doctorate were spent pricing excess-of-loss and stop-loss treaties at a Nordic reinsurer, and the problem that changed her work was two portfolios that matched in mean and variance and were priced alike, while one of them paid far more above the retention. Finding out why led her to stop-loss transforms, to the convex order, and to the old results of Hardy, Littlewood and Pólya that explain both.

From there the questions widened: what an aggregate of dependent risks can be at worst, which premium principles and which risk measures respect the orders, why a stop-loss contract is the best a risk-averse buyer can do for a given price, and what “more risk” and “more unequal” mean in economics.

The thread through her work is that these are one theory. Each order is a class of functions, each comparison is a theorem about every decision maker in that class, and comonotonicity is the worst case that dependence can reach.

She writes for readers who want the comparisons proved and then used. Every theorem in her books names the order it lives in and the class of decision makers it speaks for.

She spent her first years after it in industrial device simulation, where she learned that a carrier density which dips below zero for one time step can stop a week of computing. She then moved to a fusion research group and worked on the electron distribution of a hot plasma, where the scheme of Chang and Cooper was born, and where she learned to count the particles at every step. Later she joined a computational neuroscience collaboration, computing the population density of integrate-and-fire neurons and the firing rate that flows out through its threshold.

The equation was the same in all three places: a Fokker–Planck equation, carrying mass, positivity, an equilibrium and an entropy that only decreases. So were the failures. A scheme that kept those properties gave answers that could be trusted; a scheme that only had a small error did not.

She now teaches numerical analysis and consults on scientific software. She writes for graduate students and working scientists who want every scheme derived and every property proved on the grid, not only in the limit. Her advice to anyone writing a solver is short: count the mass, check the minimum, and compare with an exact solution before you believe a picture.

When the shelf’s producers began selling their gas company by company, he moved to the sales side. There he spent a decade on long-term contracts that let the buyer take more gas on cold days and less on warm ones, within daily and annual limits, and on storage capacity booked in caverns on the Continent. He learned that a contract’s flexibility and a cavern’s are the same thing written in different clauses, and that both are options a spreadsheet will undervalue.

A spell with a hydropower producer completed the picture. A reservoir is a cavern filled by the weather, and the price at which a producer should release its water, the water value, is a Bellman equation that Norwegian engineers were solving before most of finance had heard of one.

He now works independently in Stavanger, advising on storage, contracts and batteries, and teaches a short course for engineers moving onto the commercial side. His advice to newcomers is to read the cavern’s operating manual before the price data, and to write the value function before anything else.

He came to the subject through optimal stopping. His early work was on free-boundary problems, the curves that separate the region where one waits from the region where one acts, and on the conditions, smooth fit above all, that pin those curves down. From there the questions led naturally to stochastic control: the dynamic programming principle, the Hamilton–Jacobi–Bellman equation, and the viscosity solutions that keep the theory honest when the value function refuses to be smooth.

The thread that runs through his work is the search for the point where two theories turn out to be one. This book follows that thread into games. When every player of a large crowd solves a control problem against all the others, the backward equation of one player’s value and the forward equation of the crowd’s law stop being two problems: the equilibrium is the single fixed point that solves both.

He writes for readers who want the arguments complete. Every theorem in his books is proved, and every proof is tested on a case simple enough to solve by hand. He believes that a reader who has watched a free boundary appear as the limit of a control’s switching set will never again mistake it for a guess.

He moved to London for a decade of catastrophe reinsurance. There he learned what a capital model assumes when it lets claims arrive as a Poisson stream, and what happens to it when a storm season sends them in families. A later spell on an energy risk desk showed him the same pattern in gas prices, where one spike makes the next more likely. In 2020 he joined a group estimating reproduction numbers from daily case counts, and found himself, again, measuring the share of events that other events had caused.

That share, the branching ratio, is the thread of his work. Seismologists call it productivity, epidemiologists call it the reproduction number, and market people call it endogeneity; it decides whether a cascade dies out or runs away. He came to the Hawkes process as a practitioner, and stayed for the mathematics that makes one model serve so many trades.

He writes for working analysts and graduate students who want each result derived, each estimator fitted to a public record, and each fit tested before it is trusted. His advice to anyone new to event data is short: plot the counts first, and let the baseline move before you believe the excitement.

She came to probability through simulation. Her first serious problem was an importance sampler whose estimates looked perfectly reasonable while its variance was infinite, and finding out why led her to Girsanov’s theorem and to relative entropy, the quantity that prices every change of measure on path space. From there the questions widened: conditioning a diffusion on its endpoint, on a rare event, on a whole law at the final time; the small-noise limit in which the cost becomes an action and the likely path becomes a curve.

The thread through her work is that these are one theory. Conditioning is a drift; the best drift is the cheapest one in relative entropy; and a single variational formula, the Boué–Dupuis representation, says why. This book grew out of the moment she noticed that three drifts she had computed for three different problems were the same function.

She writes for readers who want the formulas proved and then watched at work. Every theorem in her books comes with a path you can draw, and every simulation with a check you can run.

Dr. Zamrik is drawn to the places where an abstract structure turns out to be the honest tool for a concrete problem: where a resolvent estimate, not an eigenfunction expansion, is what actually controls an evolution; where the semigroup one would like to write down does not exist, and the resolvent must stand in its place. He regards the resolvent as the more fundamental of the two objects, and much of his work is an argument for that view — carried through the non-autonomous, fractional, and fully nonlinear cases where it becomes not a preference but a necessity.

He writes in a deliberately rigorous register, favouring complete arguments over gestures and stating plainly where a method’s advantage ends. He works quietly and apart, and prefers his mathematics to speak for him.

She moved onto the paper side in her late twenties, joining the risk team of an oilseed and grain desk in Geneva. The traders had intuition; what they did not have was a model that told them how wrong they could be. She built it. Over eleven years she became the person the desk came to before a position was sized — not to be told the price, but to be told the distribution of prices, and where the position sat in its left tail.

Her scars are specific. A long new-crop corn book sized off a flat forecast that ignored the way volatility ramps into the US growing season. A soybean crush spread hedged on a model calibrated to the old-crop curve, so the harvest break in the forward curve quietly unwound the hedge. A cocoa exposure that looked diversified until a single West-African supply shock proved it was one weather system in a trench coat.

She now works independently, building simulation and risk frameworks for trading houses and merchants who have outgrown spreadsheet fair-values but distrust black boxes. She writes everything so the trader who has to run it can read it. Her first instruction to anyone new on a desk: price the distribution, not the number, and size for the tail you did not forecast.

She holds a PhD in mathematical statistics from Uppsala University and is a fellow of Svenska Aktuarieföreningen. She has been the sign-off reserving actuary on approximately one hundred and forty year-end reserve reviews and the lead capital actuary on twelve internal-model approval submissions to the Finansinspektionen and BaFin.

Her opinion, formed across two and a half decades: the bootstrap prediction error and Mack’s prediction error are not the same number. Anyone who quotes one as the other is either confused or lying.

She holds a PhD in biostatistics from the Karolinska Institute, has been the sign-off statistician on roughly four hundred clinical trials, and has negotiated more FDA Type C meetings than she cares to count.

Her opinion, formed across three decades of post-hoc protocol reviews: the operating-characteristics table is the only document that survives a regulator interaction unchanged, so it should be written first. Most “missing data” problems are estimand problems wearing a missing-data mask.

She is preoccupied with a distinction she believes the field routinely blurs — the difference between a tool that is slow and a tool that cannot express the problem. The first is an engineering inconvenience and invites an argument about hardware. The second is a structural fact and ends the conversation. Most of her writing is an attempt to establish which of the two is actually on the table, and she is unwilling to claim the second where only the first is true.

He is, by temperament, a verifier. The habit was forced on him early by a stress calculation that looked entirely reasonable and was entirely wrong — the elements had locked, and nothing on the screen said so. It never left him. When DOLFINx arrived and the finite-element community began migrating off the legacy FEniCS stack onto a faster, cleaner, still-stabilizing library, he saw both the opportunity and the danger: a new tool is exactly when old verification habits lapse.

This book is his answer. It solves partial differential equations with DOLFINx and the FEniCSx stack, and it verifies every method the same way he always has — by the method of manufactured solutions, by confirmed convergence orders, by analytic matches on the simple shapes that have them, and by physical conservation on the irregular parts that do not. He is now retired from teaching and writes on computational mechanics.

He is, by temperament, a verifier. The habit was forced on him early by a boundary-layer calculation that converged cleanly to the wrong answer, and it never left. When physics-informed neural networks arrived, he watched the field with interest and suspicion in equal measure. The networks were genuinely new and genuinely useful — they reached dimensions his grids never could. But they were also unproven in a way he found intolerable: a trained network offers no error certificate, and a wrong one looks exactly like a right one until you check it.

This book is his answer to that intolerance. It solves partial differential equations with neural networks, and it checks every solution against the Monte Carlo estimator that probability theory provides for free — and it is candid about the cases where no such check exists, and the method must therefore be trusted less. He is now retired from teaching and writes on scientific computing.

For most of those years the hardest part of every project was the same: deriving, implementing, and debugging the adjoint equations that supply the gradient. She wrote adjoints by hand, checked them against finite differences, and watched projects stall for months on a single sign error in a chain rule. When reverse-mode automatic differentiation matured into tools a working scientist could actually use, she recognized it for what it was — not a machine-learning fashion, but a quiet revolution in how the adjoint method is practiced. The gradient that once cost a graduate student a season now came, exact, almost for free. The mathematics did not change; the labor did.

Her teaching and her writing grew out of that shift. She is known for a plain, exacting style: she motivates a tool only by what it measurably buys, states the mathematics precisely, and refuses to let a reconstruction stand without the verification that earns it — the gradient check, the convergence study, the honest error bar. She is equally clear about the limits. When a problem is low-dimensional, or has a clean closed-form Jacobian, or yields to a dedicated solver, she says so and reaches for the classical method. That candor — knowing when a program should not be differentiated through at all — is, in her view, the mark of a practitioner rather than an enthusiast.

She writes for the working scientist who wants the method and the runnable code in one place, with nothing hand-waved and every result reproducible from the code that computed it. She lives in Poland.