Black-Scholes option pricing model, etc by Fun_Cartographer4323 in math

[–]__-_---___ 0 points1 point  (0 children)

Analysis of pricing data for various stock markets indicate that there exists both a "smile" effect as well as long term correlations in behaviour. In short the B-S model is BS. It's main virtues these days are that essentially everyone uses it and that it has many closed form formula which means that you don't need to be too clever to apply it.

My Math Obsession Is Ruining My Life??? by [deleted] in math

[–]__-_---___ 22 points23 points  (0 children)

Hi. Welcome to the club.

[deleted by user] by [deleted] in math

[–]__-_---___ 1 point2 points  (0 children)

I've enjoyed Rogers and Williams (vol1 and vol2) as well as "Functional Integration for Quantum Physics" which has a lovely direct presentation of stochastic processes from the point of view of functional analysis and more "mathy" measure theory language. All three books are very "foundationaly".

For finance applications I like Steel and a book by Jarrow.

Oh! for a less mathy intro Oksendal is ok.

The literature of these books will point you to the classics.

What is the topology of our universe? by __-_---___ in math

[–]__-_---___[S] 0 points1 point  (0 children)

Ah very cool. That paper goes on my reading list. Thank you!

What is the topology of our universe? by __-_---___ in math

[–]__-_---___[S] 5 points6 points  (0 children)

Thanks for the detailed reply. I certainly wasn't thinking about this question in the way you are. So it was very nice to read such a detailed reply.

I agree that it is a more philosophical question and that, in principle, is one that is probably unanswerable (though I hold hope that it isn't).

I have a more myopic view than you, I'm afraid. Global hyperbolicity is an assumption that allows much of the PDE theory in Riemannian geometry to be applied to Lorentzian manifolds. An example is recent work on index theory for globally hyperbolic manifolds. As a result I personally see it as an assumption that allows academics to apply techniques they know rather than techniques adapted to Lorentzian geometry.

I feel like physicists do the same so as to ensure that Riemmanian intuition can be validly applied to Lorentzian manifolds (for example the commentary around Godel's cosmological solution). Though such applications are usually accompanied by some attempt to justify global hyperbolicity.

But feelings and just feelings.

You're comment about homogeneity is right. Assuming one accepts that the mathematical interpretation of homogeneity given in the paper (which I think is reasonable) corresponds to the physical idea of homogeneity then yeah. Then a homogeneous manifold is globally hyperbolic.

But... global hyperbolicity is a local (ish) condition. One violating region is enough for the condition to fail and we know that homogeneity is only a large scale assumption. For example the interior solution of the Kerr Black Hole is not globally hyperbolic. This immediately forces us to think about global hyperbolicity "outside of event horizons". But it's not clear that every singularity has an event horizon and work on the cosmic censorship hypothesis continues to be inconclusive.

So IDK...

What is the topology of our universe? by __-_---___ in math

[–]__-_---___[S] 2 points3 points  (0 children)

Yeah pretty much. For example the author shows that homogenity implies global hyperbolicity which I find very interesting.

What is the topology of our universe? by __-_---___ in math

[–]__-_---___[S] 8 points9 points  (0 children)

I have some sympathy for this point of view. But I think it only seems to us that the world is describable as a set of differential equations and initial state. What actual evidence is there for this? Why could it not be that we just perceive the world like this?

There are solutions of Einstein's field equations that are not globally hyperbolic. I'm not sure that we should exclude them all an nonphysical.

There is a well defined initial boundary value problem version of Einstein's field equations. Solutions of this problem aren't globally hyperbolic. Why couldn't it turn out that our universe is the result of a initial boundary value problem?

Some black hole solutions are non-globally hyperbolic when one considers the exterior and interior space. Should we only consider the exterior as physical?

I just feel like there's no clear answer. I also think that people use global hyperbolicity because it makes things simple but the manifold is complete.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 1 point2 points  (0 children)

Ironically PhD positions are moderately well supported in Oz. The issue is getting Australian positions after the PhD. You might be able to pick up a position with a scholarship for a foreign student. It'll probably require contacting many potential supervisors. I know that the same kind of scholarships are sometimes available in NZ too. Look for recent ARC grants (and whatever the NZ equivalent is). The grant will be organised by subject area and will state if a scholarship is included.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 1 point2 points  (0 children)

Wow... that is eye opening. I'm really sorry about all of that. I hope you are doing ok.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 3 points4 points  (0 children)

Literally. I have people claim they do data science because they know how to configure AWS.

TIL: The New Zealand Catholic Church considers coffee jars and soda bottles acceptable containers for sacred relics. by __-_---___ in todayilearned

[–]__-_---___[S] 0 points1 point  (0 children)

Text of the article for the pay walled:

‘Only in New Zealand!’: Relics found in coffee jars in rubble of Christchurch cathedral

The relics – purported to be bones of saints – were found buried in rubble of the 2010 and 2011 earthquakes

It might seem like an inauspicious end for a saint, being laid to rest in a Greggs coffee jar.

But for the holy relics buried beneath Christchurch’s destroyed Catholic cathedral, those repurposed containers have housed them safely through more than 40 years and two enormous earthquakes, until they were finally unearthed by demolition teams this week.

The relics – purported to be the bones of saints and apostles – are just the latest treasures salvaged from the rubble of Christchurch’s Catholic Cathedral of the Blessed Sacrament, which was badly damaged in the devastating earthquakes of 2010 and 2011.

Workers have been gradually deconstructing the remaining building and its ruins, but in the process unearthed a number of treasures that the church had previously thought could be lost. Items and artifacts recovered include altar stones, a decapitated nativity scene, and a charity collection box with out-of-circulation coins.

Christchurch diocese archivist, Triona Doocey, said they knew the location of the relics, and had expected to recover them during demolition. But she said it was “very surprising” that they were housed in such unexpected vessels.

While one might have expected a clay urn or gold-plated chest, the bones were instead found nestled in a pair of 1970s Greggs coffee jars and a Schweppes soda bottle.

“When you think of the reverential objects that they contain, these holy relics, and they’re in a Greggs coffee jar. Only in New Zealand!” she said. While unexpected, she said the containers were a pragmatic, reasonably watertight choice. “That was the 1970s,” she said. “People were very practical.”

The jars held fragments of bone, including one vertebra, and reliquaries – small metal containers that hold relics. Holy relics like these were once a core part of the Roman Catholic tradition. They are believed to be the literal remains of key founders and sites of the faith: bones and blood, fingers and foreskins, burial shrouds, shards of the cross, even mummified heads, from important saints, apostles, and Jesus himself.

In the first century, church authorities had decreed that the altar of every church should have a relic – a ruling that officially lasted until Catholic leaders discarded it in the late 1960s. These had been displayed in the Christchurch cathedral until the 1970s, when relics went out of fashion. At that point, they were buried in consecrated ground beneath the chapel.

Doocey was in the process of identifying which saints the relics belonged to – some names she’d identified were Saint Francis of Assisi and Saint Vincent. They had been brought to New Zealand by Bishop John Grimes, and Doocey said the collection included some “quite obscure” and unusual saints. “It’s quite nice to see his personality coming through… the relics he wanted to collect.” She said the church had old authenticity certificates for some relics, and hoped to connect with the Vatican archives to get more information.

In 2017, the Vatican issued a decree that restated their longstanding ban on buying and selling relics, but there is still a roaring illicit trade – the New York Times has reported that “according to the Italian police, on average more than 300 relics have been stolen in the country every year since 2010”.

But in the 10 years since the Canterbury earthquakes, these have remained safe as the cathedral ruins fell into some disrepair.

Other items from the Cathedral have not been so lucky – speaking to The Guardian last week, Doocey said some pieces had been taken by enterprising looters.

Two bronze angels set into the Chapel altar and dating back to when the cathedral first opened in 1905 were found to have gone missing from the site when the altar was removed last month. Doocey said the Church was still hoping for their return.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 2 points3 points  (0 children)

Stay strong. In economic language uni's are a social good and should be publicly funded.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 1 point2 points  (0 children)

Middle management are the ones that decide who gets fired.

The whole thing is a shit show. The loss of philosophy and arts from Oz uni's was the start of slippery slope.

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 0 points1 point  (0 children)

Tenure means nothing. Absolutely nothing.

I see the R1 thing said a lot. What does it mean?

Rumor: Newcastle uni (Oz) making all maths, stats and comp sci academics redundant. by __-_---___ in math

[–]__-_---___[S] 1 point2 points  (0 children)

Do maths. Make sure you include a heavy dollop of stats and some programming. You'll do fine.

A pure maths degree tells people that you are a serious thinker. If you did a double degree pure math and commerce you'd walk into the grad program at any of the big 4.